A weighted weak type inequality for the maximal function

Sawyer, E.

doi:10.1090/S0002-9939-1985-0776188-1

A weighted weak type inequality for the maximal function
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Proc. Amer. Math. Soc. 93 (1985), 610-614 Request permission

Abstract:

We show that the operator $S = {\upsilon ^{ - 1}}M\upsilon$, where $M$ denotes the HardyLittlewood maximal operator, is of weak type (1,1) with respect to the measure $\upsilon (x)w(x)dx$ whenever $\upsilon$ and $w$ are ${A_1}$ weights. B. Muckenhoupt’s weighted norm inequality for the maximal function can then be obtained directly from the P. Jones factorization of ${A_p}$ weights using interpolation with change of measure.

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