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Session 33. Spaces of analytic functions
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Analytic families of multilinear operators
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Mieczysław Mastyło, Adam Mickiewicz University, Poland
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The talk is based on the joint work with L. Grafakos, University of Missouri,
Columbia, USA
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We prove complex interpolation theorems for analytic
families of multilinear operators defined on quasi-Banach spaces,
with explicit constants on the intermediate spaces. We obtain
analogous results for analytic families of operators defined on
spaces generated by the Calderón method applied to couples of
quasi-Banach lattices with nontrivial lattice convexity. As an
application we derive a multilinear version of Stein's classical
interpolation theorem for analytic families of operators taking
values in Lebesgue, Lorentz, and Hardy spaces. We use this theorem
to prove that the bilinear Bochner-Riesz operator is bounded from
\(L^p(\mathbb{R}^n)\times L^p(\mathbb{R}^n)\) into
\(L^{p/2}(\mathbb{R}^n)\) for \(1<p<2\).
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