Articles

GENERALIZED ORLICZ-TYPE SLICE SPACES, EXTRAPOLATION AND APPLICATIONS

  • Songbai WANG
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  • School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, China

Received date: 2020-08-27

  Revised date: 2022-05-09

  Online published: 2022-11-02

Supported by

The research was supported by the National Natural Science Foundation of China (11726622) and the Natural Science Foundation Projection of Chongqing, China (cstc2021jcyj-msxmX0705).

Abstract

We introduce a class of generalized Orlicz-type Auscher—Mourgoglou slice space, which is a special case of the Wiener amalgam. We prove versions of the Rubio de Francia extrapolation theorem in this space. As a consequence, we obtain the boundedness results for several classical operators, such as the Calderón—Zygmund operator, the Marcinkiewicz integrals, the Bochner—Riesz means and the Riesz potential, as well as variational inequalities for differential operators and singular integrals. As an application, we obtain global regularity estimates for solutions of non-divergence elliptic equations on generalized Orlicz-type slice spaces if the coefficient matrix is symmetric, uniformly elliptic and has a small (δ, R)-BMO norm for some positive numbers δ and R.

Cite this article

Songbai WANG . GENERALIZED ORLICZ-TYPE SLICE SPACES, EXTRAPOLATION AND APPLICATIONS[J]. Acta mathematica scientia, Series B, 2022 , 42(5) : 2001 -2024 . DOI: 10.1007/s10473-022-0516-y

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