Marcinkiewicz Sampling Theorem for Orlicz Spaces
Functional Analysis
2022-09-13 v1
Abstract
In the article we generalize the Marcinkiewicz sampling theorem in the context of Orlicz spaces. We establish conditions under which sampling theorem holds in terms of restricted submultiplicativity and supermultiplicativity of an -function , boundedness of the Hilbert transform and Matuszewska-Orlicz indices. In addition we give a new criterion for boundedness of Hilbert transform on Orlicz space.
Cite
@article{arxiv.2109.02368,
title = {Marcinkiewicz Sampling Theorem for Orlicz Spaces},
author = {Aleksander Pawlewicz and Michał Wojciechowski},
journal= {arXiv preprint arXiv:2109.02368},
year = {2022}
}
Comments
19 pages