http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Thu, 16 May 2013 15:12:12 +0000 http://www.hindawi.com/journals/jfsa/2013/252735/ A necessary and sufficient condition is given for a positive measure on to be a -Carleson measure. We give the predual of spaces in terms of this condition. Jizhen Zhou Copyright © 2013 Jizhen Zhou. All rights reserved. Tue, 07 May 2013 08:28:30 +0000 http://www.hindawi.com/journals/jfsa/2013/140130/ Using some potential theory tools and the Schauder fixed point theorem, we prove the existence and precise global behavior of positive continuous solutions for the competitive fractional system , in a bounded -domain in , subject to some Dirichlet conditions, where , The potential functions are nonnegative and required to satisfy some adequate hypotheses related to the Kato class of functions . Imed Bachar, Habib Mâagli, and Noureddine Zeddini Copyright © 2013 Imed Bachar et al. All rights reserved. Thu, 02 May 2013 15:29:29 +0000 http://www.hindawi.com/journals/jfsa/2013/793263/ This paper considers the initial value problems of the system of fractional differential equations and constructs two monotone sequences of upper and lower solutions. By using quasilinearization technique, monotone sequences of approximate solutions that converge quadratically to a solution are obtained. Peiguang Wang and Ying Hou Copyright © 2013 Peiguang Wang and Ying Hou. All rights reserved. Sat, 27 Apr 2013 12:22:53 +0000 http://www.hindawi.com/journals/jfsa/2013/842375/ Let be a Schrödinger operator on (), where is a nonnegative potential belonging to certain reverse Hölder class for . In this paper, we prove the boundedness of commutators generated by the higher order Riesz transform , where , which is larger than the space . Moreover, we prove that is bounded from the Hardy space into weak . Yu Liu, Lijuan Wang, and Jianfeng Dong Copyright © 2013 Yu Liu et al. All rights reserved. Mon, 22 Apr 2013 15:57:04 +0000 http://www.hindawi.com/journals/jfsa/2013/820437/ We are going to study the space of real functions defined on a bounded metric space and having growths tempered by a modulus of continuity. We prove also a sufficient condition for the relative compactness in the mentioned function space. Using that condition and the classical Schauder fixed point theorem, we show the existence theorem for some quadratic integral equations of Fredholm type in the space of functions satisfying the Hölder condition. An example illustrating the mentioned existence result is also included. Józef Banaś and Rafał Nalepa Copyright © 2013 Józef Banaś and Rafał Nalepa. All rights reserved. Thu, 18 Apr 2013 17:58:28 +0000 http://www.hindawi.com/journals/jfsa/2013/149659/ We investigate the existence of solutions for a sequential integrodifferential equation of fractional order with some boundary conditions. The existence results are established by means of some standard tools of fixed point theory. An illustrative example is also presented. Bashir Ahmad and Juan J. Nieto Copyright © 2013 Bashir Ahmad and Juan J. Nieto. All rights reserved. Thu, 18 Apr 2013 12:58:32 +0000 http://www.hindawi.com/journals/jfsa/2013/479049/ We present some results on the existence of solutions for second-order impulsive differential equations with deviating argument subject to functional initial conditions. Our results are based on Schaefer's fixed point theorem for completely continuous operators. Luigi Muglia and Paolamaria Pietramala Copyright © 2013 Luigi Muglia and Paolamaria Pietramala. All rights reserved. Wed, 17 Apr 2013 16:09:26 +0000 http://www.hindawi.com/journals/jfsa/2013/519893/ Let be a compact Hausdorff space and let be a topological involution on . In 1988, Kulkarni and Arundhathi studied Choquet and Shilov boundaries for real uniform function algebras on . Then in 2000, Kulkarni and Limaye studied the concept of boundaries and Choquet sets for uniformly closed real subspaces and subalgebras of or . In 1971, Dales obtained some properties of peak sets and p-sets for complex Banach function algebras on . Later in 1990, Arundhathi presented some results on peak sets for real uniform function algebras on . In this paper, while we present a brief account of the work of others, we extend some of their results, either to real subspaces of or to real Banach function algebras on . Davood Alimohammadi and Taher Ghasemi Honary Copyright © 2013 Davood Alimohammadi and Taher Ghasemi Honary. All rights reserved. Wed, 17 Apr 2013 08:20:48 +0000 http://www.hindawi.com/journals/jfsa/2013/579326/ Of concern are two classes of convoluted -regularized operator families: convoluted -cosine operator families and convoluted -semigroups. We obtain new and general multiplicative and additive perturbation theorems for these convoluted -regularized operator families. Two examples are given to illustrate our abstract results. Fang Li, Jin Liang, Ti-Jun Xiao, and Jun Zhang Copyright © 2013 Fang Li et al. All rights reserved. Thu, 11 Apr 2013 14:30:28 +0000 http://www.hindawi.com/journals/jfsa/2013/568202/ We establish the weighted estimates for the commutators and which are generated by the -dimensional rough Hardy operators and central BMO functions on the weighted Lebesgue spaces, the weighted Herz spaces and the weighted Morrey-Herz spaces. Furthermore, the weighted Lipschitz estimates are also obtained. Zhuanxi Ren and Shuangping Tao Copyright © 2013 Zhuanxi Ren and Shuangping Tao. All rights reserved. Thu, 11 Apr 2013 11:01:34 +0000 http://www.hindawi.com/journals/jfsa/2013/984259/ Our aim in this paper is to deal with the Sobolev embeddings for generalized Riesz potentials of functions in Morrey spaces over nondoubling measure spaces. Yoshihiro Sawano and Tetsu Shimomura Copyright © 2013 Yoshihiro Sawano and Tetsu Shimomura. All rights reserved. Wed, 10 Apr 2013 14:42:52 +0000 http://www.hindawi.com/journals/jfsa/2013/510943/ This paper mainly dealt with the exact number and global bifurcation of positive solutions for a class of semilinear elliptic equations with asymptotically linear function on a unit ball. As byproducts, some existence and multiplicity results are also obtained on a general bounded domain. Benlong Xu Copyright © 2013 Benlong Xu. All rights reserved. Tue, 09 Apr 2013 11:20:57 +0000 http://www.hindawi.com/journals/jfsa/2013/784983/ The aim of this paper is to get the boundedness of a class of sublinear operators with rough kernels on weighted Morrey spaces under generic size conditions, which are satisfied by most of the operators in classical harmonic analysis. Applications to the corresponding commutators formed by certain operators and BMO functions are also obtained. Shaoguang Shi and Zunwei Fu Copyright © 2013 Shaoguang Shi and Zunwei Fu. All rights reserved. Tue, 09 Apr 2013 10:41:53 +0000 http://www.hindawi.com/journals/jfsa/2013/628031/ Let ℙ be the space of polynomials with complex coefficients endowed with a nondiagonal Sobolev norm , where the matrix and the measure constitute a -admissible pair for . In this paper we establish the zero location and asymptotic behavior of extremal polynomials associated to , stating hypothesis on the matrix rather than on the diagonal matrix appearing in its unitary factorization. Ana Portilla, Yamilet Quintana, José M. Rodríguez, and Eva Tourís Copyright © 2013 Ana Portilla et al. All rights reserved. Tue, 09 Apr 2013 10:40:11 +0000 http://www.hindawi.com/journals/jfsa/2013/968603/ When the spatial dimensions , the initial data , and the Hamiltonian , we prove that the scattering operator is well defined in the whole energy space for nonlinear Schrödinger equation with exponential nonlinearity , where . Shuxia Wang Copyright © 2013 Shuxia Wang. All rights reserved. Wed, 03 Apr 2013 18:14:48 +0000 http://www.hindawi.com/journals/jfsa/2013/543748/ We establish uniform bounds for oscillatory singular integrals as well as oscillatory singular integral operators. We allow the singular kernel to be given by a function in the Hardy space , while such results were known previously only for kernels in log , a proper subspace of . One of our results established a bound for certain weights. At the same time, it provides a solution to an open problem in Lu (2005). H. Al-Qassem, L. Cheng, A. Fukui, and Y. Pan Copyright © 2013 H. Al-Qassem et al. All rights reserved. Wed, 03 Apr 2013 17:30:57 +0000 http://www.hindawi.com/journals/jfsa/2013/159435/ Stability is investigated for the following differential equations with nonconstant delay where , , , and and with ( is a positive constant) are continuous functions. A criterion is given for the zero solution of this delay equation being uniformly stable and asymptotically stable. Jin Liang, Tzon-Tzer Lu, and Yashan Xu Copyright © 2013 Jin Liang et al. All rights reserved. Sun, 31 Mar 2013 08:28:47 +0000 http://www.hindawi.com/journals/jfsa/2013/475103/ Homogeneous Triebel-Lizorkin spaces with full range of parameters are introduced on stratified Lie groups in terms of Littlewood-Paley-type decomposition. It is shown that the scale of these spaces is independent of the choice of Littlewood-Paley-type decomposition and the sub-Laplacian used for the construction of the decomposition. Some basic properties of these spaces are given. As the main result of this paper, boundedness of a class of singular integral operators on these function spaces is obtained. Guorong Hu Copyright © 2013 Guorong Hu. All rights reserved. Sun, 31 Mar 2013 08:23:23 +0000 http://www.hindawi.com/journals/jfsa/2013/718507/ We present the space of functions of bounded -variation in the sense of Riesz-Korenblum, denoted by κBVφ[a,b], which is a combination of the notions of bounded φ-variation in the sense of Riesz and bounded κ-variation in the sense of Korenblum. Moreover, we prove that the space generated by this class of functions is a Banach space with a given norm and we prove that the uniformly bounded composition operator satisfies Matkowski's weak condition. Mariela Castillo, Sergio Rivas, María Sanoja, and Iván Zea Copyright © 2013 Mariela Castillo et al. All rights reserved. Sun, 24 Mar 2013 11:10:49 +0000 http://www.hindawi.com/journals/jfsa/2013/932145/ We determine the principal eigenvalue of the linear problem ,  , , where and . Moreover, we investigate the existence of positive solutions for the corresponding nonlinear problem. The proofs of our main results are based upon the Krein-Rutman theorem and fixed point index theory. Dongming Yan Copyright © 2013 Dongming Yan. All rights reserved. Wed, 20 Mar 2013 09:43:06 +0000 http://www.hindawi.com/journals/jfsa/2013/691731/ We study the initial boundary value problem of the general three-component Camassa-Holm shallow water system on an interval subject to inhomogeneous boundary conditions. First we prove a local in time existence theorem and present a weak-strong uniqueness result. Then, we establish a asymptotic stabilization of this system by a boundary feedback. Finally, we obtain a result of blow-up solution with certain initial data and boundary profiles. Lixin Tian, Qingwen Yuan, and Lizhen Wang Copyright © 2013 Lixin Tian et al. All rights reserved. Wed, 20 Mar 2013 09:05:52 +0000 http://www.hindawi.com/journals/jfsa/2013/865835/ Let , and ω be in the class of Muckenhoupt. We introduce the weighted Besov-type spaces and weighted Triebel-Lizorkin-type spaces for and then establish the φ-transform characterizations of these new spaces in the sense of Frazier and Jawerth. Canqin Tang Copyright © 2013 Canqin Tang. All rights reserved. Wed, 20 Mar 2013 08:36:52 +0000 http://www.hindawi.com/journals/jfsa/2013/426459/ We obtain the multiplicative perturbation theorems for convoluted -cosine functions (resp., convoluted -semigroups) and -times integrated -cosine functions (resp., -times integrated -semigroups) for . Moreover, we obtain some new results for perturbations on -cosine functions (resp., -semigroups). Some examples are presented. Fang Li, Huiwen Wang, and Jun Zhang Copyright © 2013 Fang Li et al. All rights reserved. Tue, 19 Mar 2013 14:46:43 +0000 http://www.hindawi.com/journals/jfsa/2013/407425/ Manuel Ruiz Galán, María Isabel Berenguer, Gabriel N. Gatica, and Davide La Torre Copyright © 2013 Manuel Ruiz Galán et al. All rights reserved. Tue, 19 Mar 2013 09:11:16 +0000 http://www.hindawi.com/journals/jfsa/2013/567970/ This paper is concerned with the existence and nonexistence of positive solutions to the singular third-order -point boundary value problem ,  , where    are constants, is a parameter, is continuous and is allowed to be singular at and . The results here essentially extend and improve some known results. Shaolin Zhou and Xiaoling Han Copyright © 2013 Shaolin Zhou and Xiaoling Han. All rights reserved. Mon, 18 Mar 2013 11:50:45 +0000 http://www.hindawi.com/journals/jfsa/2013/275702/ We prove that the space of continuous periodic functions is a set of first category in the space of almost periodic functions, and we also show that the space of almost periodic functions is a set of first category in the space of almost automorphic functions. Zhe-Ming Zheng, Hui-Sheng Ding, and Gaston M. N'Guérékata Copyright © 2013 Zhe-Ming Zheng et al. All rights reserved. Mon, 18 Mar 2013 11:34:33 +0000 http://www.hindawi.com/journals/jfsa/2013/982753/ It is known that the unimodular Fourier multipliers are bounded on all modulation spaces for . We extend such boundedness to the case of all and obtain its asymptotic estimate as t goes to infinity. As applications, we give the grow-up rate of the solution for the Cauchy problems for the free Schrödinger equation with the initial data in a modulation space, as well as some mixed norm estimates. We also study the boundedness for the operator , for the case and Finally, we investigate the boundedness of the operator for and obtain the local well-posedness for the Cauchy problem of some nonlinear partial differential equations with fundamental semigroup . Jiecheng Chen, Dashan Fan, Lijing Sun, and Chunjie Zhang Copyright © 2013 Jiecheng Chen et al. All rights reserved. Wed, 13 Mar 2013 16:21:08 +0000 http://www.hindawi.com/journals/jfsa/2013/859402/ The boundedness of the various operators on -Morrey spaces is considered in the framework of the Littlewood-Paley decompositions. First, the Littlewood-Paley characterization of -Morrey-Campanato spaces is established. As an application, the boundedness of Riesz potential operators is revisted. Also, a characterization of -Lipschitz spaces is obtained: and, as an application, the boundedness of Riesz potential operators on -Lipschitz spaces is discussed. Yasuo Komori-Furuya, Katsuo Matsuoka, Eiichi Nakai, and Yoshihiro Sawano Copyright © 2013 Yasuo Komori-Furuya et al. All rights reserved. Tue, 12 Mar 2013 17:42:44 +0000 http://www.hindawi.com/journals/jfsa/2013/710592/ A negative solution and a positive solution are obtained for a modified capillary surface equation by variational methods. Zhanping Liang Copyright © 2013 Zhanping Liang. All rights reserved. Mon, 04 Mar 2013 10:03:50 +0000 http://www.hindawi.com/journals/jfsa/2013/578436/ We study some algebraic properties of Toeplitz operators with radial or quasihomogeneous symbols on the pluriharmonic Bergman space. We first give the necessary and sufficient conditions for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator and discuss the zero-product problem for several Toeplitz operators with radial symbols. Next, we study the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols. Finally, we also investigate finite rank commutators and semicommutators of two Toeplitz operators with quasihomogeneous symbols. Jingyu Yang, Liu Liu, and Yufeng Lu Copyright © 2013 Jingyu Yang et al. All rights reserved.