# Fractional maximal function and its commutators on Orlicz spaces

Fractional maximal function and its commutators on Orlicz spaces In this paper, we find necessary and sufficient conditions for the boundedness of fractional maximal operator $$M_{\alpha }$$ M α on Orlicz spaces. As an application of this results we consider the boundedness of fractional maximal commutator $$M_{b,\alpha }$$ M b , α and nonlinear commutator of fractional maximal operator $$[b,M_{\alpha }]$$ [ b , M α ] on Orlicz spaces, when b belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# Fractional maximal function and its commutators on Orlicz spaces

, Volume 9 (1) – Aug 23, 2017
15 pages

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Publisher
Springer Journals
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-017-0189-1
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we find necessary and sufficient conditions for the boundedness of fractional maximal operator $$M_{\alpha }$$ M α on Orlicz spaces. As an application of this results we consider the boundedness of fractional maximal commutator $$M_{b,\alpha }$$ M b , α and nonlinear commutator of fractional maximal operator $$[b,M_{\alpha }]$$ [ b , M α ] on Orlicz spaces, when b belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Aug 23, 2017

### References

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