Calderon-Zygmund singular operators in extrapolation spaces

摘要

We study the boundedness of the Hardy-Littlewood maximal operator in abstract extrapolation Banach function lattices and their Kiithe dual spaces. The extrapolation spaces are generated by compatible families of Banach function lattices on quasi-metric measure spaces with doubling measure. These results combined with a variant of the integral Coifman-Fefferman inequality imply that every Calderon-Zygmund singular operator is bounded in considered extrapolation spaces. We apply these results to extrapolation spaces determined by compatible families of Calderon-Lozanovslii spaces, in particular to compatible families of Orlicz spaces that are interpolation of weighted L-p-spaces (1 < p < infinity) with A(p) weights defined on spaces of homogeneous type. (C) 2020 Elsevier Inc. All rights reserved.