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

DOI:
https://doi.org/10.1090/S0002-9939-99-04998-9

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:
https://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