Sharp $ A 2$ Inequality for Haar Shift Operators - Mathematics > Classical Analysis and ODEsReport as inadecuate




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Abstract: As a corollary to our main theorem we give a new proof of the result that thenorm of the Hilbert transform on L^2w has norm bounded by a the A 2characteristic of a weight to the first power, a theorem of one of us. This newproof begins as the prior proofs do, by passing to Haar shifts. Then, we applya deep two-weight T1 theorem of Nazarov-Treil-Volberg, to reduce the matter tochecking a certain carleson measure condition. This condition is checked with acorona decomposition of the weight. Prior proofs of this type have used Bellmanfunctions, while this proof is flexible enough to address all Haar shifts atthe same time.



Author: Michael T. Lacey, Stefanie Petermichl, Maria Carmen Reguera

Source: https://arxiv.org/







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