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

Sawano, Yoshihiro; Shimomura, Tetsu

doi:10.1090/proc/14225

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

Proc. Amer. Math. Soc. 147 (2019), 2877-2885 Request permission

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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