$$\ell ^p\left( \mathbb {Z}^d\right) $$ 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

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Springer Berlin Heidelberg
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Mathematics; Mathematics, general
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