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GENERALIZED MORREY SPACES OVER NONHOMOGENEOUS METRIC MEASURE SPACES

Published online by Cambridge University Press:  27 October 2016

GUANGHUI LU
Affiliation:
College of Mathematics and Statistics, Northwest Normal University, 967 Anning East Road, Lanzhou 730070, PR China email [email protected]
SHUANGPING TAO*
Affiliation:
College of Mathematics and Statistics, Northwest Normal University, 967 Anning East Road, Lanzhou 730070, PR China email [email protected]
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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.

Type
Research Article
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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