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

TY - JOUR

T1 - \ell^p(\mathbb Z^d)-estimates for discrete operators of Radon type: variational estimates

AU - Mirek, Mariusz

AU - Stein, Elias M.

AU - Trojan, Bartosz

PY - 2017/1/31

Y1 - 2017/1/31

N2 - 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.

AB - 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.

U2 - 10.1007/s00222-017-0718-4

DO - 10.1007/s00222-017-0718-4

M3 - Article

SN - 0020-9910

SP - 665

EP - 748

JO - INVENTIONES MATHEMATICAE

JF - INVENTIONES MATHEMATICAE

ER -