Taiwanese Journal of Mathematics

Generalized Fractional Integral Operators and Their Commutators with Functions in Generalized Campanato Spaces on Orlicz Spaces

Minglei Shi, Ryutaro Arai, and Eiichi Nakai

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Abstract

We investigate the commutators $[b,I_{\rho}]$ of generalized fractional integral operators $I_{\rho}$ with functions $b$ in generalized Campanato spaces and give a necessary and sufficient condition for the boundedness of the commutators on Orlicz spaces. To do this we define Orlicz spaces with generalized Young functions and prove the boundedness of generalized fractional maximal operators on the Orlicz spaces.

Article information

Source
Taiwanese J. Math., Advance publication (2019), 26 pages.

Dates
First available in Project Euclid: 3 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1546506192

Digital Object Identifier
doi:10.11650/tjm/181211

Subjects
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 42B35: Function spaces arising in harmonic analysis

Keywords
Orlicz space Campanato space fractional integral commutator

Citation

Shi, Minglei; Arai, Ryutaro; Nakai, Eiichi. Generalized Fractional Integral Operators and Their Commutators with Functions in Generalized Campanato Spaces on Orlicz Spaces. Taiwanese J. Math., advance publication, 3 January 2019. doi:10.11650/tjm/181211. https://projecteuclid.org/euclid.twjm/1546506192


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