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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