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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Weighted inequalities for maximal functions associated with general measures


Author: Kenneth F. Andersen
Journal: Trans. Amer. Math. Soc. 326 (1991), 907-920
MSC: Primary 42B25
DOI: https://doi.org/10.1090/S0002-9947-1991-1038012-9
MathSciNet review: 1038012
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Abstract: For certain positive Borel measures $ \mu $ on $ {\mathbf{R}}$ and for $ {T_\mu }$ any of three naturally associated maximal function operators of Hardy-Littlewood type, the weight pairs $ (u,\upsilon)$ for which $ {T_\mu }$ is of weak type $ (p,p),1 \leq p < \infty $, and of strong type $ (p,p),1 < p < \infty $, are characterized. Only minimal assumptions are placed on $ \mu $; in particular, $ \mu $ need not satisfy a doubling condition nor need it be continuous.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1038012-9
Keywords: Maximal functions, weighted inequalities, weak type, strong type
Article copyright: © Copyright 1991 American Mathematical Society