Generalized Orlicz-Type Slice Spaces, Extrapolation and Applications

作者：Wang, Songbai^*

来源：Acta Mathematica Scientia, 2022, 42(5): 2001-2024.

DOI：10.1007/s10473-022-0516-y

• generalized Orlicz space
• extrapolation
• Hardy-Littlewood maximal operator
• Muckenhoupt weight
• variation inequality

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 Calderon-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 (delta, R)-BMO norm for some positive numbers delta and R.