On the Multilinear Fractional Integral Operators with Correlation Kernels

Abstract

In this paper, we study a class of multilinear fractional integral operators which have correlation kernels ${\prod }_{1\le i<j\le k}|x_i-x_j{|}^{-{\alpha }_{ij}}$. The necessary and sufficient conditions are obtained under which these oprators are bounded from $L^{p_1}\times \cdots \times L^{p_k}$ into $L^q$. As a consequence, we also get the endpoint estimates from $L^{p_1}\times \cdots \times L^{p_k}$ to $BMO$ of these operators.

42 pages. A new proof by Brascamp-Lieb inequality is given in this version. V1 submitted 19 Feb 2016, originally announced 19 Feb 2016

References in corpus (1)

• Multilinear Embedding and Hardy's Inequality