Resumen de Weighted estimates for bilinear fractional integral operators: a necessary and sufficient condition for power weights

Yasuo Komori-Furuya

• We consider weighted estimates for two bilinear fractional integral operators ?2,? and ???. Moen (Collect Math 60:213–238, 2009) obtained a necessary and sufficient condition for ?2,?. However we know only some sufficient conditions for ??? which is a variant of the bilinear Hilbert transform. Restricted to power weights we obtain a necessary and sufficient condition for ???. We also prove a bilinear Stein–Weiss inequality.