## Re: [harmonic] continuity of operator norms

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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
Message 1 of 3 , Oct 20, 2009
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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