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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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One-box conditions for Carleson measures for the Dirichlet space
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by Omar El-Fallah, Karim Kellay, Javad Mashreghi and Thomas Ransford PDF
Proc. Amer. Math. Soc. 143 (2015), 679-684 Request permission

Abstract:

We give a simple proof of the fact that a finite measure $\mu$ on the unit disk is a Carleson measure for the Dirichlet space if it satisfies the Carleson one-box condition $\mu (S(I))=O(\phi (|I|))$, where $\phi :(0,2\pi ]\to (0,\infty )$ is an increasing function such that $\int _0^{2\pi }(\phi (x)/x) dx<\infty$. We further show that the integral condition on $\phi$ is sharp.
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Additional Information
  • Omar El-Fallah
  • Affiliation: Laboratoire Analyse et Applications (CNRST URAC03), Université Mohamed V, B. P. 1014 Rabat, Morocco
  • MR Author ID: 338521
  • Email: elfallah@fsr.ac.ma
  • Karim Kellay
  • Affiliation: IMB, Université Bordeaux 1, 351 cours de la Libération, F-33405 Talence cedex, France
  • Email: karim.kellay@math.u-bordeaux1.fr
  • Javad Mashreghi
  • Affiliation: Département de mathématiques et de statistique, Université Laval, Québec, Canada G1V 0A6
  • MR Author ID: 679575
  • Email: javad.mashreghi@mat.ulaval.ca
  • Thomas Ransford
  • Affiliation: Département de mathématiques et de statistique, Université Laval, Québec, Canada G1V 0A6
  • MR Author ID: 204108
  • Email: ransford@mat.ulaval.ca
  • Received by editor(s): February 15, 2013
  • Received by editor(s) in revised form: April 30, 2013
  • Published electronically: September 18, 2014
  • Additional Notes: The first author was supported by Académie Hassan II des sciences et techniques
    The second author was supported by PICS-CNRS
    The third author was supported by NSERC
    The fourth author was supported by NSERC and the Canada research chairs program
  • Communicated by: Pamela B. Gorkin
  • © Copyright 2014 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 679-684
  • MSC (2010): Primary 31C25; Secondary 28C99
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12248-9
  • MathSciNet review: 3283654