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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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.