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GENERALIZED MORREY SPACES OVER NONHOMOGENEOUS METRIC MEASURE SPACES

Part of: Harmonic analysis in several variables Analysis on metric spaces

Published online by Cambridge University Press:  27 October 2016

GUANGHUI LU  and
SHUANGPING TAO
GUANGHUI LU
Affiliation:
College of Mathematics and Statistics, Northwest Normal University, 967 Anning East Road, Lanzhou 730070, PR China email lghwmm1989@126.com
SHUANGPING TAO*
Affiliation:
College of Mathematics and Statistics, Northwest Normal University, 967 Anning East Road, Lanzhou 730070, PR China email taosp@nwnu.edu.cn
*
✉taosp@nwnu.edu.cn
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Abstract

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Let $({\mathcal{X}},d,\unicode[STIX]{x1D707})$ be a nonhomogeneous metric measure space satisfying the so-called upper doubling and the geometric doubling conditions. In this paper, the authors give the natural definition of the generalized Morrey spaces on $({\mathcal{X}},d,\unicode[STIX]{x1D707})$, and then investigate some properties of the maximal operator, the fractional integral operator and its commutator, and the Marcinkiewicz integral operator.

Keywords

nonhomogeneous metric measure spacegeneralized Morrey spacemaximal operatorfractional integral operatorMarcinkiewicz integral operator

MSC classification

Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 42B35: Function spaces arising in harmonic analysis 30L99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 103 , Issue 2 , October 2017 , pp. 268 - 278
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

Footnotes

This work was supported by National Natural Foundation of China (Grant No. 11561062).

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