Characterizations of parabolic Muckenhoupt classes

Abstract

This paper extends and complements the existing theory for the parabolic Muckenhoupt weights motivated by one-sided maximal functions and a doubly nonlinear parabolic partial differential equation of p-Laplace type. The main results include characterizations for the limiting parabolic A∞ and A1 classes by applying an uncentered parabolic maximal function with a time lag. Several parabolic Calderón–Zygmund decompositions, covering and chaining arguments appear in the proofs.