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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An interpolation theorem related to
the a.e. convergence of integral operators


Author: Alexander Kiselev
Journal: Proc. Amer. Math. Soc. 127 (1999), 1781-1788
MSC (1991): Primary 42C15, 43A50; Secondary 34L40
Published electronically: February 11, 1999
MathSciNet review: 1476143
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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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

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04681-X
PII: S 0002-9939(99)04681-X
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
Article copyright: © Copyright 1999 American Mathematical Society