L^p(Z^d)-estimates for discrete operators of Radon type: Variational estimates

By Mariusz Mirek, E. Stein, Bartosz Trojan. 2015

85 citations recorded by the source corpus.

We prove $\ell^p\big(\mathbb Z^d\big)$ bounds for $p\in(1, \infty)$, of $r$-variations $r\in(2, \infty)$, 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d8bf4353cf8ba0c747a7acd38ab70e084eb9903b