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

2015/12/23 by Mariusz Mirek, Elias M. Stein, Mirek, Mariusz +3 · 1 citation
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1512.07518

openalex publication_date 2015/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove ℓ^p(\mathbb Z^d) bounds, for p∈(1, ∞), 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.

Cited by

• A Discrete Quadratic Carleson Theorem on ℓ ² with a Restricted Supremum
• L^p(Z^d)-estimates for discrete operators of Radon type: Variational estimates

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