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February 2018 A remark on modified Morrey spaces on metric measure spaces
Yoshihiro SAWANO, Tetsu SHIMOMURA, Hitoshi TANAKA}
Hokkaido Math. J. 47(1): 1-15 (February 2018). DOI: 10.14492/hokmj/1520928055

Abstract

Morrey norms, which are originally endowed with two parameters, are considered on general metric measure spaces. Volberg, Nazarov and Treil showed that the modified Hardy-Littlewood maximal operator is bounded on Legesgue spaces. The modified Hardy-Littlewood maximal operator is known to be bounded on Morrey spaces on Euclidean spaces, if we introduce the third parameter instead of adopting a natural extension of Morrey spaces. When it comes to geometrically doubling, as long as an auxiliary parameter is introduced suitably, the Morrey norm does not depend on the third parameter and this norm extends naturally the original Morrey norm. If the underlying space has a rich geometric structure, there is still no need to introduce auxiliary parameters. However, an example shows that this is not the case in general metric measure spaces. In this paper, we present an example showing that Morrey spaces depend on the auxiliary parameters.

Citation

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Yoshihiro SAWANO. Tetsu SHIMOMURA. Hitoshi TANAKA}. "A remark on modified Morrey spaces on metric measure spaces." Hokkaido Math. J. 47 (1) 1 - 15, February 2018. https://doi.org/10.14492/hokmj/1520928055

Information

Published: February 2018
First available in Project Euclid: 13 March 2018

zbMATH: 06853588
MathSciNet: MR3773722
Digital Object Identifier: 10.14492/hokmj/1520928055

Subjects:
Primary: 42B35
Secondary: 42B25

Rights: Copyright © 2018 Hokkaido University, Department of Mathematics

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Vol.47 • No. 1 • February 2018
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