%0 Journal Article
%T A geometric condition, necessity of energy, and two weight boundedness of fractional Riesz transforms
%A Eric T. Sawyer
%A Chun-Yen Shen
%A Ignacio Uriarte-Tuero
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1310.4484v3