Parabolic John–Nirenberg spaces with time lag

Abstract

We introduce a parabolic version of the so-called John–Nirenberg space that is a generalization of functions of parabolic bounded mean oscillation. Parabolic John–Nirenberg inequalities, which give weak type estimates for the oscillation of a function, are shown in the setting of the parabolic geometry with a time lag. Our arguments are based on a parabolic Calderón–Zygmund decomposition and a good lambda estimate. Chaining arguments are applied to change the time lag in the parabolic John–Nirenberg inequality.