Weighted inequalities for maximal functions associated with general measures

Andersen, Kenneth F.

doi:10.1090/S0002-9947-1991-1038012-9

Weighted inequalities for maximal functions associated with general measures
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by Kenneth F. Andersen PDF

Trans. Amer. Math. Soc. 326 (1991), 907-920 Request permission

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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