ar X iv : 1 50 1 . 05 81 8 v 5 [ m at h . C A ] 1 6 Ju l 2 01 5 AN ELEMENTARY PROOF OF THE A 2 BOUND
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چکیده
A martingale transform T , applied to an integrable locally supported function f, is pointwise dominated by a positive sparse operator applied to |f|, the choice of sparse operator being a function of T and f. As a corollary, one derives the sharp Ap bounds for martingale transforms, recently proved by Thiele-Treil-Volberg, as well as a number of new sharp weighted inequalities for martingale transforms. The (very easy) method of proof (a) only depends upon the weak-L norm of maximal truncations of martingale transforms, (b) applies in the vector valued setting, and (c) has an extension to the continuous case, giving a new elementary proof of the A2 bounds in that setting.
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تاریخ انتشار 2015