Generalized Orlicz-Type Slice Spaces, Extrapolation and Applications

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 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.

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