The Weiss conjecture and weak norms
نویسندگان
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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