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 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.