Communications in Mathematical Analysis

A Class of Parabolic Maximal Functions

Ghada Shakkah and Ahmad Al-Salman

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 17 February 2016

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)

Maximal functions Parabolic maximal functions Oscillatory integrals Singular integrals Block space


Shakkah, Ghada; Al-Salman, Ahmad. A Class of Parabolic Maximal Functions. Commun. Math. Anal. 19 (2016), no. 2, 1--31.

Export citation