A note on failure of energy reversal for classical fractional singular   integrals
  For alpha in [0,n) we demonstrate the failure of energy reversal for the vector of alpha-fractional Riesz transforms, and more generally for any vector of alpha-fractional convolution singular integrals having a kernel with vanishing integral on every great circle of the sphere. 
Eric T. Sawyer and Chun-Yen Shen and Ignacio Uriarte-Tuero
math.CA