Journal of the Mathematical Society of Japan

Strongly singular bilinear Calderón–Zygmund operators and a class of bilinear pseudodifferential operators

Árpád BÉNYI, Lucas CHAFFEE, and Virginia NAIBO

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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.

Note

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.

Article information

Source
J. Math. Soc. Japan, Volume 71, Number 2 (2019), 569-587.

Dates
Received: 26 November 2017
First available in Project Euclid: 4 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1551690077

Digital Object Identifier
doi:10.2969/jmsj/79327932

Mathematical Reviews number (MathSciNet)
MR3943451

Zentralblatt MATH identifier
07090056

Subjects
Primary: 35S05: Pseudodifferential operators 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx] 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B15: Multipliers

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

Citation

BÉNYI, Árpád; CHAFFEE, Lucas; NAIBO, Virginia. Strongly singular bilinear Calderón–Zygmund operators and a class of bilinear pseudodifferential operators. J. Math. Soc. Japan 71 (2019), no. 2, 569--587. doi:10.2969/jmsj/79327932. https://projecteuclid.org/euclid.jmsj/1551690077


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