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Universal divisors in Hardy spaces

E. AmarC. Menini — 2000

Studia Mathematica

We study a division problem in the Hardy classes H p ( ) of the unit ball of 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 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 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,...

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