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Analytic families of multilinear operators

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DMV-PTM Mathematical Meeting 17–20.09.2014, Pozna´n

Analytic families of multilinear operators

Mieczys law Masty lo

Adam Mickiewicz University, Poland mastylo@amu.edu.pl

The talk is based on the joint work with L. Grafakos, University of Missouri, Columbia, USA

Session: Spaces of analytic functions

We prove complex interpolation theorems for analytic families of multilinear operators defined on quasi-Banach spaces, with explicit constants on the in- termediate spaces. We obtain analogous results for analytic families of oper- ators defined on spaces generated by the Calder´on 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 Lp(Rn) × Lp(Rn) into Lp/2(Rn) for 1 < p < 2.

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