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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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New estimates for the maximal functions and applications
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by Óscar Domínguez and Sergey Tikhonov PDF
Trans. Amer. Math. Soc. 375 (2022), 3969-4018 Request permission


In this paper we study sharp pointwise inequalities for maximal operators. In particular, we strengthen DeVore’s inequality for the moduli of smoothness and a logarithmic variant of Bennett–DeVore–Sharpley’s inequality for rearrangements. As a consequence, we improve the classical Stein–Zygmund embedding deriving $\dot {B}^{d/p}_\infty L_{p,\infty }(\mathbb {R}^d) \hookrightarrow \text {BMO}(\mathbb {R}^d)$ for $1 < p < \infty$. Moreover, these results are also applied to establish new Fefferman–Stein inequalities, Calderón–Scott type inequalities, and extrapolation estimates. Our approach is based on the limiting interpolation techniques.
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Additional Information
  • Óscar Domínguez
  • Affiliation: Université Lyon 1, Institut Camille Jordan, 43 Blvd du 11 Novembre 1918, F-69622 Villeurbanne Cedex, France and Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain
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  • Sergey Tikhonov
  • Affiliation: Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C 08193 Bellaterra (Barcelona), Spain; ICREA, Pg. Lluív Companys 23, 08010 Barcelona, Spain, and Universitat Autònoma de Barcelona
  • MR Author ID: 706641
  • ORCID: 0000-0001-5061-4308
  • Email:
  • Received by editor(s): February 9, 2021
  • Published electronically: March 16, 2022
  • Additional Notes: The first author was partially supported by the French National Research Agency (ANR-10-LABX-0070), (ANR-11-IDEX-0007) and by MTM2017-84058-P(AEI/FEDER, UE)
    The second author was partially supported by PID2020-114948GB-I00, 2017 SGR 358, AP08856479, the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M), and the CERCA Programme of the Generalitat de Catalunya
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 3969-4018
  • MSC (2020): Primary 46E35, 42B35; Secondary 26A15, 46E30, 46B70
  • DOI:
  • MathSciNet review: 4419051