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- Title
Characterization of Lipschitz Functions via Commutators of Multilinear Singular Integral Operators in Variable Lebesgue Spaces.
- Authors
Wu, Jiang Long; Zhang, Pu
- Abstract
Let b → = (b 1 , b 2 , ... , b m) be a collection of locally integrable functions and T Σ b → the commutator of multilinear singular integral operator T. Denote by L (δ) and L (δ (⋅)) the Lipschitz spaces and the variable Lipschitz spaces, respectively. The main purpose of this paper is to establish some new characterizations of the (variable) Lipschitz spaces in terms of the boundedness of multilinear commutator T Σ b → in the context of the variable exponent Lebesgue spaces, that is, the authors give the necessary and sufficient conditions for bj (j = 1, 2, ..., m) to be L (δ) or L (δ (⋅)) via the boundedness of multilinear commutator from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces. The authors do so by applying the Fourier series technique and some pointwise estimate for the commutators. The key tool in obtaining such pointwise estimate is a certain generalization of the classical sharp maximal operator.
- Subjects
INTEGRAL operators; SINGULAR integrals; COMMUTATION (Electricity); LIPSCHITZ spaces; INTEGRABLE functions; FOURIER series
- Publication
Acta Mathematica Sinica, 2023, Vol 39, Issue 12, p2465
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-023-2164-0