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Universal divisors in Hardy spaces

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Amar E., Menini C.

Studia Mathematica

2000

tom 143

nr 1

1-21

We study a division problem in the Hardy classes $H^{p}(𝔹)$ of the unit ball 𝔹 of $ℂ^{2}$ which generalizes the $H^{p}$ corona problem, the generators being allowed to have common zeros. MPrecisely, if S is a subset of 𝔹, we study conditions on a $ℂ^{k}$-valued bounded Mholomorphic function B, with $B_{|S} = 0$, in order that for 1 ≤ p < ∞ and any function $f ∈ H^{p}(𝔹)$ with $f_{|S} = 0$ there is a $ℂ^{k}$-valued $H^{p}(𝔹)$ holomorphic function F with f = B·F, i.e. the module generated by the components of B in the Hardy class $H^{p}(𝔹)$ is the entire module $M_{S}:= {f ∈ H^{p}(𝔹): f_{|S} = 0 }$. As a special case, for S = ∅, we get the $H^{p}$ corona theorem.

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1 Studia Mathematica

1 Amar E.

1 Menini C.

1 2000

Wyniki wyszukiwania

Universal divisors in Hardy spaces