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On the Multilinear Fractional Integral Operators with Correlation Kernels (1602.06126v2)
Published 19 Feb 2016 in math.CA
Abstract: In this paper, we study a class of multilinear fractional integral operators which have correlation kernels $\prod_{1\leq i<j \leq k}|x_i-x_j|{-\alpha_{ij}}$. The necessary and sufficient conditions are obtained under which these oprators are bounded from $L{p_1}\times \cdots \times L{p_k}$ into $Lq$. As a consequence, we also get the endpoint estimates from $L{p_1}\times \cdots \times L{p_k}$ to $BMO$ of these operators.