The Weiss conjecture and weak norms

نویسندگان

  • Bernhard Hermann Haak
  • BERNHARD H. HAAK
چکیده

In this note we show that for analytic semigroups the so-called Weiss condition of uniform boundedness of the operators Re(λ) 1/2C(λ+A)−1, Re(λ) > 0 on the complex right half plane and weak Lebesgue L2,∞–admissibility are equivalent. Moreover, we show that the weak Lebesgue norm is best possible in the sense that it is the endpoint for the ’Weiss conjecture’ within the scale of Lorentz spaces Lp,q .

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تاریخ انتشار 2012