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Re: [harmonic] continuity of operator norms

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  • Josef Kirsch
    Hi, maybe I am completely wrong, but one should be able to interpolate since it is bounded on L^{2- delta}. So for a varepsilon depending on delta and the
    Message 1 of 3 , Oct 20, 2009
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      Hi,

      maybe I am completely wrong, but one should be able to interpolate
      since it is bounded on L^{2-\delta}. So for a \varepsilon depending on
      \delta and the norm on L^{2-\delta}, one gets the norm smaller than 1.

      Regards

      Josef


      Quoting mablung123 <david.cruzuribe@...>:

      > I have a linear operator T that is bounded on L^p(w), 2-\epsilon < p
      > < 2+ \epsilon, for a fixed weight w. I know that on L^2(w) the
      > operator norm of T is less than 1. Does it follow that for \epsilon
      > sufficiently small, the operator norm of T is less than 1 on L^p(w)?
      >
      > A reference would be greatly appreciated.
      >
      > David Cruz-Uribe, SFO
      >
      >



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