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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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An upper bound for the Menchov-Rademacher operator for right triangles
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by Armen Vagharshakyan PDF
Proc. Amer. Math. Soc. 150 (2022), 3959-3971 Request permission


The Menchov-Rademacher inequality is an inequality in harmonic analysis that bounds the $L_2$ norm of a certain maximal operator. It was first established in order to prove almost everywhere convergence of a one-parameter series of orthogonal functions. When two-parameter series of orthogonal functions is considered, the exact way the series is grouped becomes essential. We will consider grouping of a two-parameter series, generated by a sequence of right triangles with a vertex at the origin, who might be non-equilateral, and prove almost everywhere convergence when the eccentricity of those triangles is bounded. In order to carry out the proof, we will derive an analogue of the Menchov-Rademacher inequality for right triangles.
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Additional Information
  • Armen Vagharshakyan
  • Affiliation: Institute of Mathematics, Armenian National Academy of Sciences, Baghramyan Avenue 24/5, Yerevan 0019, Armenia
  • MR Author ID: 776347
  • ORCID: 0000-0003-4262-1019
  • Email:
  • Received by editor(s): November 11, 2020
  • Received by editor(s) in revised form: September 20, 2021, and December 10, 2021
  • Published electronically: April 7, 2022
  • Additional Notes: Research was supported by the Science Committee of Armenia, grant 18T-1A081
  • Communicated by: Dmitriy Bilyk
  • © Copyright 2022 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 150 (2022), 3959-3971
  • MSC (2020): Primary 26D15, 42B25
  • DOI:
  • MathSciNet review: 4446244