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 I_{2,\alpha } and BI_{\alpha }. Moen (Collect Math 60:213–238, 2009) obtained a necessary and sufficient condition for I_{2,\alpha }. However we know only some sufficient conditions for BI_{\alpha } which is a variant of the bilinear Hilbert transform. Restricted to power weights we obtain a necessary and sufficient condition for BI_{\alpha }. We also prove a bilinear Stein–Weiss inequality.