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