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Mathematics > Classical Analysis and ODEs

arXiv:1804.09710 (math)
[Submitted on 25 Apr 2018]

Title:Strongly singular bilinear Calderón-Zygmund operators and a class of bilinear pseudodifferential operators

Authors:Árpád Bényi, Lucas Chaffee, 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.
Comments: 18 pages, to appear in Journal of the Mathematical Society of Japan
Subjects: Classical Analysis and ODEs (math.CA)
MSC classes: 35S05, 47G30, 42B20, 42B15
Cite as: arXiv:1804.09710 [math.CA]
  (or arXiv:1804.09710v1 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.1804.09710

Submission history

From: Lucas Chaffee [view email]
[v1] Wed, 25 Apr 2018 17:56:46 UTC (15 KB)
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