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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 interpolation theorem related to the a.e. convergence of integral operators
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by Alexander Kiselev PDF
Proc. Amer. Math. Soc. 127 (1999), 1781-1788 Request permission

Abstract:

We show that for integral operators of general form the norm bounds in Lorentz spaces imply certain norm bounds for the maximal function. As a consequence, the a.e. convergence for the integral operators on Lorentz spaces follows from the appropriate norm estimates.
References
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Additional Information
  • Alexander Kiselev
  • Affiliation: Mathematical Sciences Research Institute, 5 1000 Centennial Drive, Berkeley, California 94720
  • Address at time of publication: Department of Mathematics, University of Chicago, 5734 South University Avenue, Chicago, Illinois 60637-1546
  • Email: kiselev@math.uchicago.edu
  • Received by editor(s): June 4, 1997
  • Received by editor(s) in revised form: September 17, 1997
  • Published electronically: February 11, 1999
  • Communicated by: Christopher D. Sogge
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 1781-1788
  • MSC (1991): Primary 42C15, 43A50; Secondary 34L40
  • DOI: https://doi.org/10.1090/S0002-9939-99-04681-X
  • MathSciNet review: 1476143