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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on bi-linear multipliers
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by Saurabh Shrivastava PDF
Proc. Amer. Math. Soc. 143 (2015), 3055-3061 Request permission

Abstract:

In this paper we prove that if $\chi _{_E}(\xi -\eta )$ – the indicator function of a measurable set $E\subseteq \mathbb {R}^d$ – is a bi-linear multiplier symbol for exponents $p,q,r$ satisfying the Hölder’s condition $\frac {1}{p}+\frac {1}{q}=\frac {1}{r}$ and exactly one of $p,q,$ or $r’=\frac {r}{r-1}$ is less than $2,$ then $E$ is equivalent to an open subset of $\mathbb {R}^d.$
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Additional Information
  • Saurabh Shrivastava
  • Affiliation: Department of Mathematics, Indian Institute of Science Education and Research Bhopal, Indore By-pass road Bhauri, Bhopal-462066, India
  • MR Author ID: 894393
  • Email: saurabhk@iiserb.ac.in
  • Received by editor(s): March 18, 2014
  • Published electronically: March 18, 2015
  • Communicated by: Alexander Iosevich
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 3055-3061
  • MSC (2010): Primary 42A45, 42B15; Secondary 42B25
  • DOI: https://doi.org/10.1090/S0002-9939-2015-12679-2
  • MathSciNet review: 3336630