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April, 2019 Strongly singular bilinear Calderón–Zygmund operators and a class of bilinear pseudodifferential operators
Árpád BÉNYI, Lucas CHAFFEE, Virginia NAIBO
J. Math. Soc. Japan 71(2): 569-587 (April, 2019). DOI: 10.2969/jmsj/79327932

Abstract

Motivated by the study of kernels of bilinear pseudodifferential operators with symbols in a Hörmander class of critical order, we investigate boundedness properties of strongly singular Calderón–Zygmund operators in the bilinear setting. For such operators, whose kernels satisfy integral-type conditions, we establish boundedness properties in the setting of Lebesgue spaces as well as endpoint mappings involving the space of functions of bounded mean oscillations and the Hardy space. Assuming pointwise-type conditions on the kernels, we show that strongly singular bilinear Calderón–Zygmund operators satisfy pointwise estimates in terms of maximal operators, which imply their boundedness in weighted Lebesgue spaces.

Funding Statement

The first author is partially supported by a grant from the Simons Foundation (No. 246024). The third author is partially supported by the NSF under grant DMS 1500381.

Citation

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Árpád BÉNYI. Lucas CHAFFEE. Virginia NAIBO. "Strongly singular bilinear Calderón–Zygmund operators and a class of bilinear pseudodifferential operators." J. Math. Soc. Japan 71 (2) 569 - 587, April, 2019. https://doi.org/10.2969/jmsj/79327932

Information

Received: 26 November 2017; Published: April, 2019
First available in Project Euclid: 4 March 2019

zbMATH: 07090056
MathSciNet: MR3943451
Digital Object Identifier: 10.2969/jmsj/79327932

Subjects:
Primary: 35S05 , 42B20 , 47G30
Secondary: 42B15

Keywords: bilinear pseudodifferential operators , Calderón–Zygmund operators , strongly singular bilinear operators

Rights: Copyright © 2019 Mathematical Society of Japan

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Vol.71 • No. 2 • April, 2019
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