Tohoku Mathematical Journal
2020
September
SECOND SERIES VOL. 72, NO. 3

Tohoku Math. J.
72 (2020), 335-348

Title BOUNDEDNESS OF MAXIMAL OPERATORS ON HERZ SPACES WITH RADIAL VARIABLE EXPONENT

Author Yoshihiro Mizuta and Tetsu Shimomura

(Received September 6, 2018, revised March 11, 2019)
Abstract. Our aim in this paper is to deal with the boundedness of the central Hardy-Littlewood maximal operator on Herz spaces with radial variable exponent. As a special case, we show the boundedness of the maximal operator in weighted Lebesgue spaces with radial variable exponent. We also discuss the integrability of the maximal functions in such spaces.

Mathematics Subject Classification. Primary 42B25; Secondary 46E30.
Key words and phrases. Hardy-Littlewood maximal function, radial variable exponent, Herz space.

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