article · Forum Mathematicum · 2024

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

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Abstract

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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>L</m:mi> <m:mi>p</m:mi> </m:msup> </m:math> {L^{p}} to <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>L</m:mi> <m:mi>q</m:mi> </m:msup> </m:math> {L^{q}} if and only if the locally integrable function is the sum of a constant and a function in certain Lebesgue space.

Cite this paper

APA 7

Sun, W., & Wang, S. (2024). The L p -L q compactness of commutators of oscillatory singular integrals. Forum Mathematicum. https://doi.org/10.1515/forum-2024-0316

MLA 9

Sun, Wenchang, and Shifen Wang. “The L p -L q compactness of commutators of oscillatory singular integrals.” Forum Mathematicum, 2024, https://doi.org/10.1515/forum-2024-0316.

Chicago

Sun, Wenchang, and Shifen Wang. 2024. “The L p -L q compactness of commutators of oscillatory singular integrals.” Forum Mathematicum. https://doi.org/10.1515/forum-2024-0316.

Harvard

Sun, W. and Wang, S. (2024) ‘The L p -L q compactness of commutators of oscillatory singular integrals’, Forum Mathematicum. Available at: https://doi.org/10.1515/forum-2024-0316.

BibTeX

@article{sun2024compactness,
  title = {{The <i>L</i> <sup> <i>p</i> </sup>-<i>L</i> <sup> <i>q</i> </sup> compactness of commutators of oscillatory singular integrals}},
  author = {Sun, Wenchang and Wang, Shifen},
  journal = {Forum Mathematicum},
  year = {2024},
  doi = {10.1515/forum-2024-0316}
}

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