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 $B_{q}^{0,-1/2}(\mathbb{S}^{n-1}),$ $q>1$.
Citation
Ghada Shakkah. Ahmad Al-Salman. "A Class of Parabolic Maximal Functions." Commun. Math. Anal. 19 (2) 1 - 31, 2016.
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