Complex interpolation of -norms, duality and foliations

  • Bo Berndtsson

    Chalmers University of Technology and University of Göteborg, Sweden
  • Dario Cordero-Erausquin

    Sorbonne Université, Paris, France
  • Bo'az Klartag

    The Weizmann Institute of Science, Rehovot and Tel Aviv University, Israel
  • Yanir A. Rubinstein

    University of Maryland, College Park, USA
Complex interpolation of $\mathbb R$-norms, duality and foliations cover

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The complex method of interpolation, going back to Calderón and Coifman et al., on the one hand, and the Alexander–Wermer–Słodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of interpolation of real (finite-dimensional) Banach spaces and of convex functions. The underlying duality in this method is given by the Legendre transform. Our results can also be interpreted as new properties of solutions of the homogeneous complex Monge–Ampère equation.

Cite this article

Bo Berndtsson, Dario Cordero-Erausquin, Bo'az Klartag, Yanir A. Rubinstein, Complex interpolation of -norms, duality and foliations. J. Eur. Math. Soc. 22 (2020), no. 2, pp. 477–505

DOI 10.4171/JEMS/927