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An unification of Orlicz-Morrey spaces and its applications

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Abstract

The first main result of this paper is a unified approach on the studies of Orlicz-Morrey spaces. There are at least three versions of Orlicz-Morrey spaces, the Nakai type, the Sawano-Sugano-Tanaka type and the Guliyev-Hasanov-Sawano-Noi type. This paper unifies the studies by introducing a Orlicz-Morrey spaces that include those Orlicz-Morrey spaces mentioned above. The second main result is on the applications of the Orlicz-Morrey spaces on partial differential equations. We obtain the Agmon-Douglis-Nirenberg estimates of uniformly elliptic equations, the estimates of the solutions of some nonhomogeneous quasilinear elliptic equations and the Beltrami equations on Orlicz-Morrey spaces.

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The author thanks the reviewers for their valuable suggestions which improve the presentation of this paper.

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  1. Department of Mathematics and Information Technology, The Education University of Hong Kong, 10, Lo Ping Road, Tai Po, Hong Kong, China

    Kwok-Pun Ho

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Ho, KP. An unification of Orlicz-Morrey spaces and its applications. manuscripta math. 172, 1201–1226 (2023). https://doi.org/10.1007/s00229-022-01430-x

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