Laboratoire de Mathématiques de Besançon - UMR 6623 CNRS

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Les événements de août 2020


  • Analyse Fonctionnelle

    • Mardi 25 août 13:45-15:00 - Martijn Caspers - TU Delft

      Weak type estimates for multiple operator integrals and generalized absolute value functions

      Résumé : This talk is concerned with the following question. Let f be
      an n times differentiable function on the reals with bounded n-th
      derivative. Let f_n be its n-th order divided difference function. For
      instance f_1(s,t) = (f(s) - f(t))/(s-t). Is it true that the multiple
      operator integral T_f_n maps S_p_1 times .... times S_p_n to S_1,
      boundedly ?Here S_p is the Schatten non-commutative Lp-space and
      S_1, \infty is the non-commutative weak L_1 space. In case n=1 the
      question boils down on whether the Schur multiplier with symbol
      (f_1(s,t))_s,t is bounded from S_1 to S_1, \infty. We give a
      positive answer to a class of functions involving the function a(t) =
      sign(t) t^n. If n =1 we find a complete solution and the asnwer is
      affirmative. We give further details and definitions in the talk,
      including the theory of multiple operator integrals. This is joint work
      with Fedor Sukochev, Dima Zanin as well as Denis Potapov.


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