\ell^p(\mathbb Z^d)-estimates for discrete operators of Radon type: variational estimates

Mariusz Mirek, Elias M. Stein, Bartosz Trojan

Research output: Contribution to journalArticlepeer-review

51 Citations (Scopus)

Abstract

We prove pZd bounds for p ∈ (1,∞), of r-variations r ∈(2,∞), for discrete averaging operators and truncated singular integrals of Radon type. We shall present a new powerful method which allows us to deal with these operators in a unified way and obtain the range of parameters of p and r which coincide with the ranges of their continuous counterparts.
Original languageEnglish
Pages (from-to)665–748
Number of pages84
JournalINVENTIONES MATHEMATICAE
Early online date31 Jan 2017
DOIs
Publication statusE-pub ahead of print - 31 Jan 2017

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