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arXiv · 1512.07518

$\ell^p\big(\mathbb Z^d\big)$-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimates

Mariusz Mirek·Elias M. Stein·Bartosz Trojan
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Abstract

We prove $\ell^p\big(\mathbb Z^d\big)$ bounds, for $p\in(1, \infty)$, of discrete maximal functions corresponding to averaging operators and truncated singular integrals of Radon type, and their applications to pointwise ergodic theory. Our new approach is based on a unified analysis of both types of operators, and also yields an extension to the vector-valued form of these results.

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Mariusz Mirek, Elias M. Stein, Bartosz Trojan. 2015-12-23. $\ell^p\big(\mathbb Z^d\big)$-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimates. https://arxiv.org/abs/1512.07518

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