Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 71, Number 2 (2019), 569-587.
Strongly singular bilinear Calderón–Zygmund operators and a class of bilinear pseudodifferential operators
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.
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.
J. Math. Soc. Japan, Volume 71, Number 2 (2019), 569-587.
Received: 26 November 2017
First available in Project Euclid: 4 March 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35S05: Pseudodifferential operators 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx] 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B15: Multipliers
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