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Maximal operator on Orlicz spaces of two variable exponents over unbounded quasi-metric measure spaces


Authors: Yoshihiro Sawano and Tetsu Shimomura
Journal: Proc. Amer. Math. Soc. 147 (2019), 2877-2885
MSC (2010): Primary 42B25; Secondary 46E30
DOI: https://doi.org/10.1090/proc/14225
Published electronically: April 3, 2019
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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.


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Yoshihiro Sawano
Affiliation: Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachioji, 192-0397, Japan
Email: yoshihiro-sawano@celery.ocn.ne.jp

Tetsu Shimomura
Affiliation: Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan
Email: tshimo@hiroshima-u.ac.jp

DOI: https://doi.org/10.1090/proc/14225
Keywords: Maximal operator, variable exponent, quasi-metric measure spaces, non-doubling measure
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
Article copyright: © Copyright 2019 American Mathematical Society