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A weighted weak type inequality for the maximal function
1985
Proceedings of the American Mathematical Society
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We show that the operator S = v~lMv, where M denotes the Hardy-Littlewood maximal operator, is of weak type (1,1) with respect to the measure v(x)w(x) dx whenever v and w are A¡ weights. B. Muckenhoupt's weighted norm inequality for the maximal function can then be obtained directly from the P. Jones factorization of Ap weights using interpolation with change of measure. In [8], B. Muckenhoupt characterized the nonnegative functions, or weights, w on R satisfying the weighted norm inequality (1 < p < oo)
doi:10.1090/s0002-9939-1985-0776188-1
fatcat:mmiqhbaowrbevcphmtino4esyi