TY - JOUR T1 - A Characterization of Approximation of Hardy Operators in VLS AU - Akın, Lütfi PY - 2018 DA - September DO - 10.18466/cbayarfbe.449954 JF - Celal Bayar University Journal of Science JO - CBUJOS PB - Manisa Celal Bayar University WT - DergiPark SN - 1305-130X SP - 333 EP - 336 VL - 14 IS - 3 LA - en AB - Variable exponent spaces and Hardy operator space haveplayed an important role in recent harmonic analysis because they have aninteresting norm including both local and global properties. The variableexponent Lebesgue spaces are of interest for their applications to modelingproblems in physics, and to the study of variational integrals and partial differentialequations with non-standard growth conditions. This studiesalso has beenstimulated by problemsof elasticity, fluiddynamics, calculus of variations, anddifferential equations withnon-standard growth conditions. In this study, we will discussa characterization of approximation ofHardy operators in variable Lebesgue spaces. KW - Variable exponent KW - Hardy operator KW - Sobolev space CR - 1. Bernstein, S, N, Demonstration du teoreme de Weirerstrass, fondee sur le calcul des probabilites, Communication Society Mathematics, 1913, 13. CR - 2. Berens, H, Lorentz, G, G, Inverse theorems for Bernstein polynomials, Indiana University Mathematics Journal, 1972, 21, 693-708. CR - 3. Berens, H, DeVore, R,A, Quantitative Korovkin theorems for positive linear operators on Lp spaces, Transactions American Mathematical Society, 1978, 245, 349-361. CR - 4. Ditzian, Z, Totik, V, Moduli of Smoothness, Springer, Series in Computational Mathematics, Springer-Verlag, 1987, (9). CR - 5. Bing-Zheng, L, Bo-Lu, H, Ding-Xuan Z, Approximation on Variable Exponent Spaces by Linear Integral Operators, Journal of Approximation Theory, 2017, 223, 29-51. CR - 6. Orlicz,W, Uber konjugierte Exponentenfolgen, Studia Mathematica, 1931, 3, 200-211. CR - 7. Acerbi, E, Mingione, G, Regularity results for a class of functionals with nonstandard growth, Archive for Rational Mechanics and Analysis, 2001, 156, 121-140. CR - 8. Blomgren, P, Chan, T, Mulet, P, Wong, C, K, Total variation image restoration: numerical methods and extensions, Proceedings of the 1997 IEEE International Conference on Image Processing, 1997, 3, 384-387. CR - 9. Bollt, E, M, Chartrand, R, Esedoglu, S, Schultz, P, Vixie, K, R, Graduated adaptive image denoising: local compromise between total variation and isotropic diffusion, Advance Computational Mathematics, 2009, 31, 61-85. CR - 10. Chen,Y, Levine, S, Rao, M, Variable exponent linear growth functionals in image restoration, SIAM Journal of Applied Mathematics, 2006, 66, 1383-1406 CR - 11. Mamedov,F, Zeren,Y, Akın, L, Compactification of weighted Hardy operator in variable exponent Lebesgue spaces, Asian Journal of Mathematics and Computer Science, 2017, 17:1, 38-47. CR - 12. Fan, X, L, Zhao, D, On the spaces Lp(x) and Wm;p(x), Journal of Mathematic Analysis and Applications, 2001, 263, 424-446. CR - 13. Diening, L, Harjulehto, P, Hastö, P, Ruzicka, M, Lebesgue and Sobolev Spaces with Variable Exponents, Springer-Verlag, Berlin/Heidelberg, 2011. CR - 14. Stein, E, M, Singular Integrals and Dierentiability Properties of Functions, Princeton University Press, Princeton, New Jersey, 1970. UR - https://doi.org/10.18466/cbayarfbe.449954 L1 - https://dergipark.org.tr/en/download/article-file/545275 ER -