Hardy operators on Musielak–Orlicz spaces
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Turhan Karaman
Abstract
In this paper, we study the boundedness of the Hardy operators on Musielak–Orlicz spaces.
Acknowledgements
The author would like to thank the referees for their helpful suggestions and comments.
References
[1] L. Diening, Maximal function on Musielak–Orlicz spaces and generalized Lebesgue spaces, Bull. Sci. Math. 129 (2005), no. 8, 657–700. 10.1016/j.bulsci.2003.10.003Search in Google Scholar
[2] L. Diening, P. Harjulehto, P. Hästö and M. Růžička, Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Math. 2017, Springer, Heidelberg, 2011. 10.1007/978-3-642-18363-8Search in Google Scholar
[3] P. Harjulehto and P. Hästö, The Riesz potential in generalized Orlicz spaces, Forum Math. 29 (2017), no. 1, 229–244. 10.1515/forum-2015-0239Search in Google Scholar
[4] P. Harjulehto, P. Hästö and R. Klén, Generalized Orlicz spaces and related PDE, Nonlinear Anal. 143 (2016), 155–173. 10.1016/j.na.2016.05.002Search in Google Scholar
[5] P. A. Hästö, The maximal operator on generalized Orlicz spaces, J. Funct. Anal. 269 (2015), no. 12, 4038–4048. 10.1016/j.jfa.2015.10.002Search in Google Scholar
[6] P. A. Hästö, Corrigendum to “The maximal operator on generalized Orlicz spaces” [J. Funct. Anal. 269 (2015) 4038–4048] [MR3418078], J. Funct. Anal. 271 (2016), no. 1, 240–243. 10.1016/j.jfa.2016.04.005Search in Google Scholar
[7] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer, Berlin, 1983. 10.1007/BFb0072210Search in Google Scholar
[8] W. Orlicz, Über eine gewisse Klasse von Raumen vom Typus B, Bull. Int. Acad. Pol. Ser. A 8 (1932), 207–220. Search in Google Scholar
[9] L.-E. Persson and N. Samko, Weighted Hardy and potential operators in the generalized Morrey spaces, J. Math. Anal. Appl. 377 (2011), no. 2, 792–806. 10.1016/j.jmaa.2010.11.029Search in Google Scholar
[10] N. Samko, Weighted Hardy and singular operators in Morrey spaces, J. Math. Anal. Appl. 350 (2009), no. 1, 56–72. 10.1016/j.jmaa.2008.09.021Search in Google Scholar
[11] N. Samko, Weighted Hardy and potential operators in Morrey spaces, J. Funct. Spaces Appl. 2012 (2012), Article ID 678171. 10.1155/2012/678171Search in Google Scholar
[12] E. M. Stein and R. Shakarchi, Real Analysis. Measure Theory, Integration, and Hilbert Spaces, Princeton Lect. Anal. 3, Princeton University Press, Princeton, 2005. 10.1515/9781400835560Search in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Upper bounds for geodesic periods over rank one locally symmetric spaces
- Additive bases with coefficients of newforms
- A note on split extensions of bialgebras
- Petersson norm of cusp forms associated to real quadratic fields
- A realization theorem for sets of lengths in numerical monoids
- On the non-existence of the Mackey topology for locally quasi-convex groups
- The Davies method revisited for heat kernel upper bounds of regular Dirichlet forms on metric measure spaces
- The cup product of Brooks quasimorphisms
- Heat kernel estimates for time fractional equations
- Extreme non-Arens regularity of the group algebra
- Rational homology and homotopy of high-dimensional string links
- Global integrability for solutions to some anisotropic problem with nonstandard growth
- Hardy operators on Musielak–Orlicz spaces
- Contractibility of the stability manifold for silting-discrete algebras
- Order of the canonical vector bundle over configuration spaces of spheres
- An endpoint version of uniform Sobolev inequalities
- Space-time L2 estimates, regularity and almost global existence for elastic waves
- k-spaces and duals of non-archimedean metrizable locally convex spaces
- Path homology theory of multigraphs and quivers
Articles in the same Issue
- Frontmatter
- Upper bounds for geodesic periods over rank one locally symmetric spaces
- Additive bases with coefficients of newforms
- A note on split extensions of bialgebras
- Petersson norm of cusp forms associated to real quadratic fields
- A realization theorem for sets of lengths in numerical monoids
- On the non-existence of the Mackey topology for locally quasi-convex groups
- The Davies method revisited for heat kernel upper bounds of regular Dirichlet forms on metric measure spaces
- The cup product of Brooks quasimorphisms
- Heat kernel estimates for time fractional equations
- Extreme non-Arens regularity of the group algebra
- Rational homology and homotopy of high-dimensional string links
- Global integrability for solutions to some anisotropic problem with nonstandard growth
- Hardy operators on Musielak–Orlicz spaces
- Contractibility of the stability manifold for silting-discrete algebras
- Order of the canonical vector bundle over configuration spaces of spheres
- An endpoint version of uniform Sobolev inequalities
- Space-time L2 estimates, regularity and almost global existence for elastic waves
- k-spaces and duals of non-archimedean metrizable locally convex spaces
- Path homology theory of multigraphs and quivers
