A weighted weak type inequality for the maximal function

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.