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

Mariusz Mirek; Elias M. Stein; Bartosz Trojan

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

Classical Analysis and ODEs 2018-10-31 v2

Authors: Mariusz Mirek , Elias M. Stein , Bartosz Trojan

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.

Keywords

discrete operators Radon type maximal functions vector-valued estimates $\ell^p$ bounds pointwise ergodic theory singular integrals

Cite

@article{arxiv.1512.07518,
  title  = {$\ell^p\big(\mathbb Z^d\big)$-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimates},
  author = {Mariusz Mirek and Elias M. Stein and Bartosz Trojan},
  journal= {arXiv preprint arXiv:1512.07518},
  year   = {2018}
}

Comments

31 pages. Major revision. To appear in the Journal of Functional Analysis

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

Abstract

Keywords

Cite

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