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Results tagged with hardy-spaces
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user 153260
2
votes
Accepted
Criteria for Hardy space membership
This actually holds for all $p>0$. The function \begin{equation} G[f](\zeta):=\Big( \int_0^1(1-r)|f'(r\zeta)|^2 dr \Big)^{\frac 12}\end{equation}
is sometimes called Paley Littlewood $g$-function. Th …
3
votes
0
answers
187
views
Beurling's theorem on invariant subspaces
Beurling's theorem characterize the closed subspaces $M\subset H^2$ of the Hardy space, which are invariant under the shift operator $Sf(z):=zf(z)$, as spaces of the form $\varphi H^2 $ where $\varphi …
3
votes
Accepted
Example of an $H^1$ function on the bidisk that is not a product of two $H^2$ functions
I asked the polydisc experts for a reference and in fact it is known. It was proved by by J.P. Rosay in this paper. It is in french but it shouldn't be difficult to understand.