# Universal divisors in Hardy spaces

Studia Mathematica (2000)

- Volume: 143, Issue: 1, page 1-21
- ISSN: 0039-3223

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topAmar, E., and Menini, C.. "Universal divisors in Hardy spaces." Studia Mathematica 143.1 (2000): 1-21. <http://eudml.org/doc/216806>.

@article{Amar2000,

abstract = {We study a division problem in the Hardy classes $H^\{p\}()$ of the unit ball 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 , 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 $f ∈ H^\{p\}()$ with $f_\{|S\} = 0$ there is a $ℂ^\{k\}$-valued $H^\{p\}()$ holomorphic function F with f = B·F, i.e. the module generated by the components of B in the Hardy class $H^\{p\}()$ is the entire module $M_\{S\}:= \{f ∈ H^\{p\}(): f_\{|S\} = 0 \}$. As a special case, for S = ∅, we get the $H^\{p\}$ corona theorem.},

author = {Amar, E., Menini, C.},

journal = {Studia Mathematica},

keywords = {Hardy space; unit ball; divisors; corona problem},

language = {eng},

number = {1},

pages = {1-21},

title = {Universal divisors in Hardy spaces},

url = {http://eudml.org/doc/216806},

volume = {143},

year = {2000},

}

TY - JOUR

AU - Amar, E.

AU - Menini, C.

TI - Universal divisors in Hardy spaces

JO - Studia Mathematica

PY - 2000

VL - 143

IS - 1

SP - 1

EP - 21

AB - We study a division problem in the Hardy classes $H^{p}()$ of the unit ball 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 , 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 $f ∈ H^{p}()$ with $f_{|S} = 0$ there is a $ℂ^{k}$-valued $H^{p}()$ holomorphic function F with f = B·F, i.e. the module generated by the components of B in the Hardy class $H^{p}()$ is the entire module $M_{S}:= {f ∈ H^{p}(): f_{|S} = 0 }$. As a special case, for S = ∅, we get the $H^{p}$ corona theorem.

LA - eng

KW - Hardy space; unit ball; divisors; corona problem

UR - http://eudml.org/doc/216806

ER -

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