Sharp weighted inequalities for

the vector-valued maximal function

Author:
Carlos Pérez

Journal:
Trans. Amer. Math. Soc. **352** (2000), 3265-3288

MSC (1991):
Primary 42B20, 42B25, 42B15

DOI:
https://doi.org/10.1090/S0002-9947-99-02573-8

Published electronically:
November 18, 1999

MathSciNet review:
1695034

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove in this paper some sharp weighted inequalities for the vector-valued maximal function of Fefferman and Stein defined by

where is the Hardy-Littlewood maximal function. As a consequence we derive the main result establishing that in the range there exists a constant such that

Furthermore the result is sharp since cannot be replaced by . We also show the following endpoint estimate

where is a constant independent of .

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Additional Information

**Carlos Pérez**

Affiliation:
Departmento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Email:
carlos.perez@uam.es

DOI:
https://doi.org/10.1090/S0002-9947-99-02573-8

Received by editor(s):
May 19, 1997

Published electronically:
November 18, 1999

Additional Notes:
This work was partially supported by DGICYT grant PB940192, Spain

Article copyright:
© Copyright 2000
American Mathematical Society