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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.
Inventiones mathematicae – Springer Journals
Published: Jan 31, 2017
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