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Multilinear fractional Calder\'on-Zygmund operators on weighted Hardy spaces
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We prove norm estimates for multilinear fractional integrals acting on weighted and variable Hardy spaces. In the weighted case we develop ideas we used for multilinear singular integrals [7]. For the variable exponent case, a key element of our proof is a new multilinear, off-diagonal version of the Rubio de Francia extrapolation theorem.
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Multilinear Fractional Integral Operators: A counter-example
A counterexample proves that the multilinear fractional integral operator Iγ does not map H^1(R) × H^p(R) into H^q(R) for 0 < p ≤ γ^{-1} and 1/q = 1 + 1/p − γ.
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