Maximal operator on Orlicz spaces of two variable exponents over unbounded quasi-metric measure spaces
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- by Yoshihiro Sawano and Tetsu Shimomura PDF
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Abstract:
In this paper, we are concerned with the boundedness of the Hardy-Littlewood maximal operator on the Orlicz space $L^{p(\cdot )}(\log L)^{q(\cdot )}(X)$ of two variable exponents over unbounded quasi-metric measure spaces, as an extension of [Math Scand. 116 (2015), pp. 5–22]. The result is new even for the variable exponent Lebesgue space $L^{p(\cdot )}(X)$ in that the underlying spaces need not be bounded and that the underlying measure need not be doubling.References
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Additional Information
- Yoshihiro Sawano
- Affiliation: Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachioji, 192-0397, Japan
- MR Author ID: 766323
- Email: yoshihiro-sawano@celery.ocn.ne.jp
- Tetsu Shimomura
- Affiliation: Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan
- MR Author ID: 356757
- Email: tshimo@hiroshima-u.ac.jp
- Received by editor(s): December 30, 2017
- Received by editor(s) in revised form: April 19, 2018
- Published electronically: April 3, 2019
- Communicated by: Svitlana Mayboroda
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 2877-2885
- MSC (2010): Primary 42B25; Secondary 46E30
- DOI: https://doi.org/10.1090/proc/14225
- MathSciNet review: 3973891