## Communications in Mathematical Analysis

### A Class of Parabolic Maximal Functions

#### Abstract

In this paper, we prove $L^{p}$ estimates of a class of parabolic maximal functions provided that their kernels are in $L^{q}$. Using the obtained estimates, we prove the boundedness of the maximal functions under very weak conditions on the kernel. In particular, we prove the$\ L^{p}$-boundedness of our maximal functions when their kernels are in $L\log L^{\frac{1}{2}}(\mathbb{S}^{n-1})$ or in the block space $B_{q}^{0,-1/2}(\mathbb{S}^{n-1}),$ $q>1$.

#### Article information

Source
Commun. Math. Anal., Volume 19, Number 2 (2016), 1-31.

Dates
First available in Project Euclid: 17 February 2016