Abstract
Abstract This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq (S n−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.
Highlights
An active topic of current research is the investigation on the variational inequalities for various operators
This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces
We establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq(Sn− ) (q > ) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces
Summary
An active topic of current research is the investigation on the variational inequalities for various operators. We are interested in two types of results: – Boundedness and compactness properties for variation operators of singular integrals with rough kernels and their commutators on Morrey spaces. – Boundedness and continuity properties for variation operators of Calderón-Zygmund singular integrals and their commutators on Besov spaces.
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