GENERALIZED ORLICZ-TYPE SLICE SPACES, EXTRAPOLATION AND APPLICATIONS

doi:10.1007/s10473-022-0516-y

摘要/Abstract

摘要： 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.

关键词: generalized Orlicz space, extrapolation, Hardy—Littlewood maximal operator, Muckenhoupt weight, variation inequality

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.

Key words: generalized Orlicz space, extrapolation, Hardy—Littlewood maximal operator, Muckenhoupt weight, variation inequality

中图分类号:

46E30

Songbai WANG. GENERALIZED ORLICZ-TYPE SLICE SPACES, EXTRAPOLATION AND APPLICATIONS[J]. 数学物理学报(英文版), 2022, 42(5): 2001-2024.

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

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