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Two-weighted estimations for the
Hardy-Littlewood maximal function
in ideal Banach spaces


Author: E. I. Berezhnoi
Journal: Proc. Amer. Math. Soc. 127 (1999), 79-87
MSC (1991): Primary 42B20, 42B25
MathSciNet review: 1622773
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Abstract: We give conditions on a couple of ideal Banach spaces with weights which are both necessary and sufficient for the Hardy-Littlewood maximal function to satisfy the two-weighted estimations of weak type, and we consider a modification of the Hardy-Littlewood maximal function. We also give some conditions on weights in order for the Hardy-Littlewood maximal function and the modification under consideration to fulfil the two-weighted estimations of strong type.


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Additional Information

E. I. Berezhnoi
Email: smirn@gw.yspu.yar.ru

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04998-9
Received by editor(s): December 11, 1991
Received by editor(s) in revised form: September 19, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1999 American Mathematical Society