Boundedness and compactness characterizations of Cauchy integral commutators on Morrey spaces

By Jin Tao, Dachun Yang, D. Yang. Mathematical methods in the applied sciences, 2018

65 citations recorded by the source corpus.

Let CΓ be the Cauchy integral operator on a Lipschitz curve Γ. In this article, the authors show that the commutator [b,CΓ] is bounded (resp, compact) on the Morrey space Lp,λ(R) for any (or some) p  ∈  (1,∞) and λ  ∈  (0,1) if and only if b∈BMO(R) (resp, CMO(R) ). As an application, a factorization of the classical Hardy space H1(R) in terms of CΓ and its adjoint operator is obtained.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bb96a4fec71f887766311a89adf7acbc3e3d34a8

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In Applied Mathematics

1. Ji Li
2. Xuan Thinh Duong
3. Peng Chen
4. Lixin Yan
5. Dachun Yang
6. P. Auscher
7. T. Coulhon
8. S. Hofmann

In Mathematical Physics

1. Ji Li
2. Xuan Thinh Duong
3. Peng Chen
4. Lixin Yan
5. T. Coulhon
6. Dachun Yang
7. P. Auscher
8. S. Hofmann

Citations in the corpus

• Compactness of Riesz transform commutator on stratified Lie groups (2018, background): “ositive real line, the Cauchy’s integrals on the real line, the Calder´on– Zygmund operator associated with homogeneous kernels Ω(x) |x|n on R n, and the multilinear Riesz transforms, see for example [4, 9, 13, 17, 18, 19, 23] and related references therein. Beyond these operators in the Euclidean s”