%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