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The L p -L q compactness of commutators of oscillatory singular integrals

  • Wenchang Sun and Shifen Wang EMAIL logo
Published/Copyright: November 14, 2024

Abstract

We study the compactness of commutator of a locally integrable function and an oscillatory singular integral operator defined by a real-valued polynomial and a kernel function satisfying the Hölder condition. We show that such a commutator is compact from L p to L q if and only if the locally integrable function is the sum of a constant and a function in certain Lebesgue space.

MSC 2020: 42B20; 42B35

Communicated by Christopher D. Sogge


Award Identifier / Grant number: 12171250

Award Identifier / Grant number: U21A20426

Award Identifier / Grant number: 12271267

Funding statement: This work was partially supported by the National Natural Science Foundation of China (12171250, U21A20426 and 12271267).

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Received: 2024-07-07
Revised: 2024-10-04
Published Online: 2024-11-14
Published in Print: 2025-06-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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