A weighted weak type inequality for the maximal function Journal Articles

We show that the operator S = υ − 1 M υ S = {\upsilon ^{ - 1}}M\upsilon , where M M denotes the HardyLittlewood maximal operator, is of weak type (1,1) with respect to the measure υ ( x ) w ( x ) d x \upsilon (x)w(x)dx whenever υ \upsilon and w w are A 1 {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 {A_p} weights using interpolation with change of measure.