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
DOI:
https://doi.org/10.1090/S0002-9939-99-04681-X
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.
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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:
https://doi.org/10.1090/S0002-9939-99-04681-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