A geometric condition, necessity of energy, and two weight boundedness of fractional Riesz transforms

2013/10/16 by Eric T. Sawyer, Chun-Yen Shen, Sawyer, Eric T. +3
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math #math.CA

paper · pdf · doi:10.48550/arxiv.1310.4484

21 pages. We thank Michael Lacey for pointing out our failure to address the weak boundedness property in an earlier version. This version uses the corrected theorem in arXiv:1302.5093v7, which in turn uses the Lacey-Wick Monotonicity Lemma

arxiv created 2014/03/16 · arxiv updated 2014/03/18

Abstract

We prove that the energy conditions in arXiv:1302.5093v7 are implied by the fractional A2 conditions and testing conditions for the vector of fractional Riesz transforms when one measure is supported on a line. Then we apply the main theorem in arXiv:1302.5093v7 to obtain a T1 theorem for the fractional Riesz transforms when one weight is supported on a line.

Citations

• A two weight theorem for fractional singular integrals with an energy side condition and quasicube testing

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