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Universal divisors in Hardy spaces

E. Amar, C. Menini (2000)

Studia Mathematica

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,...

Wold decomposition of the Hardy space and Blaschke products similar to a contraction

M. Stessin (1999)

Colloquium Mathematicae

The classical Wold decomposition theorem applied to the multiplication by an inner function leads to a special decomposition of the Hardy space. In this paper we obtain norm estimates for componentwise projections associated with this decomposition. An application to operators similar to a contraction is given.

Currently displaying 101 – 120 of 124