A general maximal operator and the 𝐴_{𝑝}-condition

Leckband, M. A.; Neugebauer, C. J.

doi:10.1090/S0002-9947-1983-0682735-3

A general maximal operator and the $A_{p}$-condition
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by M. A. Leckband and C. J. Neugebauer PDF

Trans. Amer. Math. Soc. 275 (1983), 821-831 Request permission

Abstract:

A rearrangement inequality for a general maximal operator $Mf(x) = {\sup _{x \in Q}}\int {f\phi _{Q} d\nu }$ is established. This is then applied to the Hardy-Littlewood maximal operator with weights.

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A note on the equivalence of

and Sawyer’s condition for equal weights

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