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Mixed-norm spaces and interpolation

Joaquín OrtegaJoan Fàbrega — 1994

Studia Mathematica

Let D be a bounded strictly pseudoconvex domain of n with smooth boundary. We consider the weighted mixed-norm spaces A δ , k p , q ( D ) of holomorphic functions with norm f p , q , δ , k = ( | α | k ʃ 0 r 0 ( ʃ D r | D α f | p d σ r ) q / p r δ q / p - 1 d r ) 1 / q . We prove that these spaces can be obtained by real interpolation between Bergman-Sobolev spaces A δ , k p ( D ) and we give results about real and complex interpolation between them. We apply these results to prove that A δ , k p , q ( D ) is the intersection of a Besov space B s p , q ( D ) with the space of holomorphic functions on D. Further, we obtain several properties of the mixed-norm...

Sur une extension du problème de Gleason dans les domaines pseudoconvexes

Joaquin M. Ortega — 1984

Annales de l'institut Fourier

Dans cet article on montre que toute f A ( D ) a une décomposition f ( z ) - f ( w ) = i = 1 n g i ( z , w ) ( z i - w i ) avec g i A ( D × D ) pour les domaines pseudoconvexes à frontière réelle-analytique et aussi pour les domaines pseudoconvexes pour lesquels le résultat soit valable localement.

On quotients of holomorphic funtions in the dics with boundary regularity conditions.

Joaquín M. Ortega — 1988

Publicacions Matemàtiques

In this paper we give characterizations of those holomorphic functions in the unit disc in the complex plane that can be written as a quotient of functions in A(D), A(D) or Λ(D) with a nonvanishing denominator in D. As a consequence we prove that if f ∈ Λ(D) does not vanish in D, then there exists g ∈ Λ(D) which has the same zero set as f in Dbar and such that fg ∈ A(D).

Division and extension in weighted Bergman-Sobolev spaces.

Joaquín M. OrtegaJoan Fàbrega — 1992

Publicacions Matemàtiques

Let D be a bounded strictly pseudoconvex domain of Cn with C boundary and Y = {z; u1(z) = ... = ul(z) = 0} a holomorphic submanifold in the neighbourhood of D', of codimension l and transversal to the boundary of D. In this work we give a decomposition formula f = u1f1 + ... + ulfl for functions f of the Bergman-Sobolev space...

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