http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2012, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/713534/We find the best constants in inequalities relating the standard norm, the dual norm, and the norm ∥x∥(p,s):=inf⁡{∑k∥x(k)∥p,s}, where the infimum is taken over all finite representations x=∑kx(k) in the classical Lorentz sequence spaces. A crucial point in this analysis is the concept of level sequence, which we introduce and discuss. As an application, we derive the best constant in the triangle inequality for such spaces.S. Barza, A. N. Marcoci, and L. E. PerssonCopyright © 2012 S. Barza et al. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/905650/We determine, via classroom proofs, the maximal ideal space, the Bass stable rank as well as the topological and dense stable rank of the uniform closure of all complex-valued functions continuously differentiable on neighborhoods of a compact planar set K and holomorphic in the interior K∘ of K. In this spirit, we also give elementary approaches to the calculation of these stable ranks for some classical function algebras on K.Raymond Mortini and Rudolf RuppCopyright © 2012 Raymond Mortini and Rudolf Rupp. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/208741/We establish, in dimension two, a regularity result for nonnegative solutions to an adjoint elliptic equation, generalizing a previous result of Escauriaza (1994). We consider elliptic equations with coefficients aij(x1,x2) which are measurable with respect to one variable and VMO with respect to the other.Teresa AlbericoCopyright © 2012 Teresa Alberico. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/426067/Let Φ be an N-function. We show that a function u∈LΦ(ℝn) belongs to the Orlicz-Sobolev space W1,Φ(ℝn) if and only if it satisfies the (generalized) Φ-Poincaré inequality. Under more restrictive assumptions on Φ, an analog of the result holds in a general metric measure space setting.Toni HeikkinenCopyright © 2012 Toni Heikkinen. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/678171/We study the weighted p→q-boundedness of Hardy-type operators in Morrey spaces ℒp,λ(ℝn) (or ℒp,λ(ℝ+1) in the one-dimensional case) for a class of almost monotonic weights. The obtained results are applied to a similar weighted p→q-boundedness of the Riesz potential operator. The conditions on weights, both for the Hardy and potential operators, are necessary and sufficient in the case of power weights. In the case of more general weights, we provide separately necessary and sufficient conditions in terms of Matuszewska-Orlicz indices of weights.Natasha SamkoCopyright © 2012 Natasha Samko. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/982360/Let G0 and G∞ be, respectively, bounded and unbounded components of a plane curve Γ satisfying Dini's smoothness condition. In addition to partial sum of Faber series of f belonging to weighted Smirnov-Orlicz space EM,ω (G0), we prove that interpolating polynomials and Poisson polynomials are near best approximant for f. Also considering a weighted fractional moduli of smoothness, we obtain direct and converse theorems of trigonometric polynomial approximation in Orlicz spaces with Muckenhoupt weights. On the bases of these approximation theorems, we prove direct and converse theorems of approximation, respectively, by algebraic polynomials and rational functions in weighted Smirnov-Orlicz spaces EM,ω(G0) and EM,ω(G∞).Ramazan AkgünCopyright © 2010 Ramazan Akgün. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/202987/We introduce and study the concept of (p,k)-variation (1<p<∞, k∈N) of a real function on a compact interval. In particular, we prove that a function u:[a,b]→R has bounded (p,k)-variation if and only if u(k-1) is absolutely continuous on [a,b] and u(k) belongs to Lp[a,b]. Moreover, an explicit connection between the (p,k)-variation of u and the Lp-norm of u(k) is given which is parallel to the classical Riesz formula characterizing functions in the spaces RVp[a,b] and Ap[a,b]. This may also be considered as an alternative characterization of the one variable Sobolev space Wpk[a,b].N. Merentes, S. Rivas, and J. L. SanchezCopyright © 2012 N. Merentes et al. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/265092/For C1-functions f, given in the complex space Cn, integral representations of the form f=P(f)−T(∂¯f) are obtained. Here, P is the orthogonal projector of the space L2{Cn;e−σ|z|ρ|z|γdm(z)} onto its subspace of entire functions and the integral operator T appears by means of explicitly constructed kernel Φ which is investigated in detail.Arman H. KarapetyanCopyright © 2012 Arman H. Karapetyan. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/179015/Let L=−Δ+V be a Schrödinger operator on ℝn, where V∈Lloc1(ℝn) is a nonnegative function on ℝn. In this article, we show that the Hardy spaces L on product spaces can be characterized in terms of the Lusin area integral, atomic decomposition, and maximal functions.Liang Song and Chaoqiang TanCopyright © 2012 Liang Song and Chaoqiang Tan. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/876315/We study a flexible method for constructing curvelet-type frames. These curvelet-type systems have the same sparse representation properties as curvelets for appropriate classes of smooth functions, and the flexibility of the method allows us to give a constructive description of how to construct curvelet-type systems with a prescribed nature such as compact support in direct space. The method consists of using the machinery of almost diagonal matrices to show that a system of curvelet molecules which is sufficiently close to curvelets constitutes a frame for curvelet-type spaces. Such a system of curvelet molecules can then be constructed using finite linear combinations of shifts and dilates of a single function with sufficient smoothness and decay.Kenneth N. Rasmussen and Morten NielsenCopyright © 2012 Kenneth N. Rasmussen and Morten Nielsen. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/643458/We study the homogenization of a parabolic equation with oscillations in both space and time in the coefficient a(x/ε,t/ε2) in the elliptic part and spatial oscillations in the coefficient ρ(x/ε) that is multiplied with the time derivative ∂tuε. We obtain a strange term in the local problem. This phenomenon appears as a consequence of the combination of the spatial oscillation in ρ(x/ε) and the temporal oscillation in a(x/ε,t/ε2) and disappears if either of these oscillations is removed.L. Flodén, A. Holmbom, and M. Olsson LindbergCopyright © 2012 L. Flodén et al. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/382932/We solve the inhomogeneous simple harmonic oscillator equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the simple harmonic oscillator equation.Soon-Mo Jung and Byungbae KimCopyright © 2012 Soon-Mo Jung and Byungbae Kim. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/474681/Necessary and sufficient conditions on weight pairs guaranteeing the two-weight inequalities for the potential operators (Iαf)(x)=∫0∞(f(t)/|x−t|1−α)dt and (ℐα1,α2f)(x,y)=∫0∞∫0∞(f(t,τ)/|x−t|1−α1|y−τ|1−α2)dtdτ on the cone of nonincreasing functions are derived. In the case of ℐα1,α2, we assume that the right-hand side weight is of product type. The same problem for other mixed-type double potential operators is also studied. Exponents of the Lebesgue spaces are assumed to be between 1 and ∞.Alexander Meskhi and Ghulam MurtazaCopyright © 2012 Alexander Meskhi and Ghulam Murtaza. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/328310/The paper deals with unconditional wavelet bases in weighted Lp spaces. Inhomogeneous wavelets of Daubechies type are considered. Necessary and sufficient conditions for weights are found for which the wavelet system is an unconditional basis in weighted Lp spaces in dependence on p.Agnieszka WojciechowskaCopyright © 2012 Agnieszka Wojciechowska. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/737534/We give a decomposition for the dual space of some Banach Function Spaces as the Zygmund space EXPα of the exponential integrable functions, the Marcinkiewicz space Lp,∞, and the Grand Lebesgue Space Lp),θ.Claudia Capone and Maria Rosaria FormicaCopyright © 2012 Claudia Capone and Maria Rosaria Formica. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/643135/Differential operators generated by homogeneous functions ψ of an arbitrary real order s>0 (ψ-derivatives) and related spaces of s-smooth periodic functions of d variables are introduced and systematically studied. The obtained scale is compared with the scales of Besov and Triebel-Lizorkin spaces. Explicit representation formulas for ψ-derivatives are obtained in terms of the Fourier transform of their generators. Some applications to approximation theory are discussed.Konstantin Runovski and Hans-Jürgen SchmeisserCopyright © 2012 Konstantin Runovski and Hans-Jürgen Schmeisser. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/527647/We analyze the existence of (no past) exponential dichotomies for a well-posed autonomous differential equation (that generates a C0-semigroup {T(t)}t≥0). The novelty of our approach consists in the fact that we do not assume the T(t)-invariance of the unstable manifolds. Roughly speaking, we prove that if the solution of the corresponding inhomogeneous difference equation belongs to any sequence space (on which the right shift is an isometry) for every inhomogeneity from the same class of sequence spaces, then the continuous-time solutions of the autonomous homogeneous differential equation will exhibit a (no past) exponential dichotomic behavior. This approach has many advantages among which we emphasize on the facts that the aforementioned condition is very general (since the class of sequence spaces that we use includes almost all the known sequence spaces, as the classical ℓp spaces, sequence Orlicz spaces, etc.) and that from discrete-time conditions we get information about the continuous-time behavior of the solutions.Răzvan O. Moşincat, Ciprian Preda, and Petre PredaCopyright © 2012 Răzvan O. Moşincat et al. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/659761/We state and prove a new refined Boas-type inequality in a setting with a topological space and general σ-finite and finite Borel measures. As a consequence of the result obtained, we derive a new class of Hardy- and Pólya-Knopp-type inequalities related to balls in ℝn and prove that constant factors involved in their right-hand sides are the best possible.A. Cižmešija, J. Pecaric, and D. PokazCopyright © 2012 A. Čižmešija et al. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/314068/We study Kadec-Klee properties with respect to global (local) convergence in measure. First, we present some results concerning Köthe spaces and Orlicz functions. Next, we shall give full criteria for Kadec-Klee properties with respect to global (local) convergence in measure in Calderón-Lozanovskiĭ function spaces. In particular, we obtain the full characterizations of Kadec-Klee properties in Orlicz-Lorentz function spaces, which have not been presented until now.Paweł KolwiczCopyright © 2012 Paweł Kolwicz. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/894527/Let C(n)(D×D¯) be a Banach space of complex-valued functions f(x,y) that are continuous on D×D¯, where D={z∈C:|z|<1} is the unit disc in the complex plane C, and have nth partial derivatives in D×D which can be extended to functions continuous on D×D¯, and let CA(n)=CA(n)(D×D) denote the subspace of functions in C(n)(D×D¯) which are analytic in D×D (i.e., CA(n)=C(n)(D×D¯)∩Hol(D×D)). The double integration operator is defined in CA(n) by the formula Wf(z,w)=∫0z∫0wf(u,v)dv du. By using the method of Duhamel product for the functions in two variables, we describe the commutant of the restricted operator W∣Ezw, where Ezw={f∈CA(n):f(z,w)=f(zw)} is an invariant subspace of W, and study its properties. We also study invertibility of the elements in CA(n) with respect to the Duhamel product.Suna Saltan and Yasemin ÖzelCopyright © 2012 Suna Saltan and Yasemin Özel. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/693251/We introduce the Besov-Schatten spaces Bp(ℓ2), a matrix version af analytic Besov space, and we compute the dual of this space showing that it coincides with the matricial Bloch space introduced previously in Popa (2007). Finally we compute the space of all Schur multipliers on B1(ℓ2).A. N. Marcoci, L. G. Marcoci, and L. E. PerssonCopyright © 2012 A. N. Marcoci et al. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/542607/A new summability method of series is introduced and studied. The particular cases of this method are, for example, variable-order Cesaro and Riesz methods. Applications to divergence problem of Fourier series are given. An extension of Kolmogorov, Schipp, and Bočkarev’s well-known theorems on divergence of Fourier trigonometric, Walsh, and orthonormal series is established.Shakro TetunashviliCopyright © 2012 Shakro Tetunashvili. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/328908/We present characterizations of the Besov-type spaces Bp,qs,τ and the Triebel-Lizorkin-type spaces Fp,qs,τ by differences. All these results generalize the existing classical results on Besov and Triebel-Lizorkin spaces by taking τ=0.Douadi DrihemCopyright © 2012 Douadi Drihem. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/174856/We estimate the measure of nonconvex total boundedness in terms of simpler quantitative characteristics in the space of measurable functions  L0. A Fréchet-Smulian type compactness criterion for convexly totally bounded subsets of L0 is established.Marianna Tavernise and Alessandro TrombettaCopyright © 2012 Marianna Tavernise and Alessandro Trombetta. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/361807/We will prove the duality and reflexivity of variable exponent Triebel-Lizorkin and Besov spaces. It was shown by many authors that variable exponent Triebel-Lizorkin spaces coincide with variable exponent Bessel potential spaces, Sobolev spaces, and Lebesgue spaces when appropriate indices are chosen. In consequence of the results, these variable exponent function spaces are shown to be reflexive.Takahiro NoiCopyright © 2012 Takahiro Noi. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/145491/We give a sharp estimate on the norm of the scaling operator Uλf(x)=f(λx) acting on the weighted modulation spaces Ms,tp,q(ℝd). In particular, we recover and extend recent results by Sugimoto and Tomita in the unweighted case. As an application of our results, we estimate the growth in time of solutions of the wave and vibrating plate equations, which is of interest when considering the well-posedness of the Cauchy problem for these equations. Finally, we provide new embedding results between modulation and Besov spaces.Elena Cordero and Kasso A. OkoudjouCopyright © 2012 Elena Cordero and Kasso A. Okoudjou. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/148706/In a recent work of the author, a parabolic extension of the elliptic Ogawa type inequality has been established. This inequality is originated from the Brézis-Gallouët-Wainger logarithmic type inequalities revealing Sobolev embeddings in the critical case. In this paper, we improve the parabolic version of Ogawa inequality by allowing it to cover not only the class of functions from Sobolev spaces, but also the wider class of Hölder continuous functions.H. IbrahimCopyright © 2012 H. Ibrahim. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/853232/We study noneffective weights in the framework of variable exponent Lebesgue spaces, and we show that Lp(⋅)(Ω)=Lωp(⋅)(Ω) if and only if ω(x)1/p(x)~constant in the set where p(⋅)<∞, and ω(x)~constant in the set where p(⋅)=∞.Alberto Fiorenza and Miroslav KrbecCopyright © 2012 Alberto Fiorenza and Miroslav Krbec. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/780382/Necessary and sufficient conditions for the existence of variational principles for a given wide class of evolutionary differential-difference operator equation are obtained. The theoretic results are illustrated by two examples.I. A. Kolesnikova and V. M. SavchinCopyright © 2012 I. A. Kolesnikova and V. M. Savchin. All rights reserved.http://www.hindawi.com/journals/jfsa/2012/582726/The main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Kaczmarz series does not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of L log+ L(I2), the set of the functions the logarithmic means of quadratical partial sums of the double Walsh-Kaczmarz series of which converge in measure is of first Baire category.Ushangi Goginava and Károly NagyCopyright © 2012 Ushangi Goginava and Károly Nagy. All rights reserved.