Estimates for Brascamp-Lieb forms in weighted $L^p$-spaces. 

 

We discuss a family of Brascamp-Lieb forms where we can give (almost) necessary and sufficient conditions for the boundedness of the form on weighted $L^p$-spaces with power weights. The weighted spaces we consider are the the spaces $L^p_\lambda$ for which $ |x|^\lambda f(x)$ lies in $L^p$. Our results imply the Stein-Weiss theorem on fractional integration in the $L^p_\lambda$. These results are joint with Carl Lee and Katharine Ott.