# $$\ell ^p\left( \mathbb {Z}^d\right)$$ ℓ p Z d -estimates for discrete operators of Radon type: variational estimates

$$\ell ^p\left( \mathbb {Z}^d\right)$$ ℓ p Z d -estimates for discrete operators... We prove $$\ell ^p\left( {\mathbb {Z}}^d\right)$$ ℓ p Z d bounds for $$p\in (1, \infty )$$ p ∈ ( 1 , ∞ ) , of r-variations $$r\in (2, \infty )$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Inventiones mathematicae Springer Journals

# $$\ell ^p\left( \mathbb {Z}^d\right)$$ ℓ p Z d -estimates for discrete operators of Radon type: variational estimates

, Volume 209 (3) – Jan 31, 2017
84 pages

/lp/springer_journal/ell-p-left-mathbb-z-d-right-p-z-d-estimates-for-discrete-operators-of-Fw6W0UkHJk
Publisher
Springer Berlin Heidelberg
Subject
Mathematics; Mathematics, general
ISSN
0020-9910
eISSN
1432-1297
D.O.I.
10.1007/s00222-017-0718-4
Publisher site
See Article on Publisher Site

### Abstract

We prove $$\ell ^p\left( {\mathbb {Z}}^d\right)$$ ℓ p Z d bounds for $$p\in (1, \infty )$$ p ∈ ( 1 , ∞ ) , of r-variations $$r\in (2, \infty )$$ 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.

### Journal

Inventiones mathematicaeSpringer Journals

Published: Jan 31, 2017

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