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Linked References

1. D. E. Edmunds, V. Kokilashvili, and A. Meskhi, Bounded and Compact Integral Operators, vol. 543, Kluwer Academic, Dordrecht, The Netherlands, 2002.
2. V. Kokilashvili, A. Meskhi, and L.-E. Persson, Weighted Norm Inequalities for Integral Transforms with Product Kernels, Nova Science, New York, NY, USA, 2010.
3. A. Kufner, L. Maligranda, and L.-E. Persson, The Hardy Inequality—About Its History and Some Related Results, Pilsen, Czech, 2007.
4. A. Kufner and L.-E. Persson, Weighted Inequalities of Hardy Type, World Scientific, River Edge, NJ, USA, 2003.
5. D. Lukkassen, A. Medell, L.-E. Persson, and N. Samko, “Hardy and singular operators in weighted generalized Morrey spaces with applications to singular integral equations,” Mathematical Methods in the Applied Sciences, vol. 35, no. 11, pp. 1300–1311, 2012.
6. H. Triebel, “Entropy and approximation numbers of limiting embeddings—an approach via Hardy inequalities and quadratic forms,” Journal of Approximation Theory, vol. 164, no. 1, pp. 31–46, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
7. L.-E. Persson and N. Samko, “Weighted Hardy and potential operators in the generalized Morrey spaces,” Journal of Mathematical Analysis and Applications, vol. 377, no. 2, pp. 792–806, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
8. N. Samko, “Weighted Hardy and singular operators in Morrey spaces,” Journal of Mathematical Analysis and Applications, vol. 350, no. 1, pp. 56–72, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
9. N. Samko, “Weighted Hardy and potential operators in Morrey spaces,” Journal of Function Spaces and Applications, vol. 2012, Article ID 678171, 21 pages, 2012. View at Publisher · View at Google Scholar
10. M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton University Press, Princeton, NJ, USA, 1983.
11. A. Kufner, O. John, and S. Fučík, Function Spaces, Noordhoff International, Leyden, Mass, USA, 1977.
12. M. E. Taylor, Tools for PDE: Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials, vol. 81 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 2000.
13. H. Rafeiro, N. Samko, and S. Samko, “Morrey-Campanato spaces: an overview,” in Operator Theory, Pseudo-Differential Equations, and Mathematical Physics, Birkhäuser Mathematics.
14. G. T. Dzhumakaeva and K. Zh. Nauryzbaev, “Lebesgue-Morrey spaces,” Izvestiya Akademii Nauk Kazakhskoĭ SSR. Seriya Fiziko-Matematicheskaya, no. 5, pp. 7–12, 1982 (Russian). View at Zentralblatt MATH
15. C. T. Zorko, “Morrey space,” Proceedings of the American Mathematical Society, vol. 98, no. 4, pp. 586–592, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
16. V. Guliyev, Integral operators on function spaces on homogeneous groups and on domains in ℝⁿ [Ph.D. thesis], Steklov Mathematical Institute, Moscow, Russia, 1994.
17. V. Guliyev, Function Spaces, Integral Operators and Two Weighted Inequalities on Homogeneous Groups, Some applications, Baku, Azerbaijan, 1999.
18. V. I. Burenkov, H. V. Guliyev, and V. S. Guliyev, “On boundedness of the fractional maximal operator from complementary Morrey-type spaces to Morrey-type spaces,” in The Interaction of Analysis and Geometry, vol. 424 of Contemporary Mathematics, pp. 17–32, American Mathematical Society, Providence, RI, USA, 2007.
19. V. Guliyev, J. Hasanov, and S. Samko, “Maximal, potential and singular operators in the local “complementary” variable exponent Morrey type spaces,” Journal of Mathematical Analysis and Applications. In press.
20. N. K. Bari and S. B. Stečkin, “Best approximations and differential properties of two conjugate functions,” Proceedings of the Moscow Mathematical Society, vol. 5, pp. 483–522, 1956 (Russian).
21. N. K. Karapetyants and N. Samko, “Weighted theorems on fractional integrals in the generalized Hölder spaces $H_0^{\omega }(\rho )$ via indices $m_{\omega }$ and $M_{\omega }$,” Fractional Calculus & Applied Analysis, vol. 7, no. 4, pp. 437–458, 2004. View at Zentralblatt MATH
22. S. G. Kreĭn, Ju. I. Petunin, and E. M. Semënov, Interpolation of Linear Operators, Nauka, Moscow, Russia, 1978.
23. L. Maligranda, “Indices and interpolation,” Dissertationes Mathematicae, vol. 234, p. 49, 1985. View at Zentralblatt MATH
24. W. Matuszewska and W. Orlicz, “On some classes of functions with regard to their orders of growth,” Studia Mathematica, vol. 26, pp. 11–24, 1965. View at Zentralblatt MATH
25. L.-E. Persson, N. Samko, and P. Wall, “Quasi-monotone weight functions and their characteristics and applications,” Mathematical Inequalities and Applications, vol. 12, no. 3, pp. 685–705, 2012.
26. N. Samko, “Singular integral operators in weighted spaces with generalized Hölder condition,” Proceedings of A. Razmadze Mathematical Institute, vol. 120, pp. 107–134, 1999. View at Zentralblatt MATH
27. N. Samko, “On non-equilibrated almost monotonic functions of the Zygmund-Bary-Stechkin class,” Real Analysis Exchange, vol. 30, no. 2, pp. 727–745, 2004/2005.
28. L. Maligranda, Orlicz Spaces and Interpolation, Departamento de Matemática, Universidade Estadual de Campinas, Campinas, Brazil, 1989.
29. N. G. Samko, S. G. Samko, and B. G. Vakulov, “Weighted Sobolev theorem in Lebesgue spaces with variable exponent,” Journal of Mathematical Analysis and Applications, vol. 335, no. 1, pp. 560–583, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH