Lᵖ(Zᵈ)-estimates for discrete operators of Radon type: Variational estimates

الأصل · EN

We prove ℓᵖ(Zᵈ) 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.