Parabolic local Campanato estimates for commutators of parabolic fractional maximal and integral operators with rough kernel

Abstract

In this paper, the author introduces parabolic generalized local Morrey spaces and parabolic local Campanato spaces, respectively and also establishes parabolic local Campanato estimates for commutators of parabolic fractional maximal and integral operators with rough kernel on parabolic generalized local Morrey spaces. As its special cases, the corresponding results of commutators of parabolic fractional maximal and integral operators with rough kernel can be deduced, respectively. As an application, we obtain the boundedness characterizations of commutators of parabolic fractional powers of some analytic semigroups on parabolic generalized local Morrey spaces.