Displaying similar documents to “Complex tangential characterizations of Hardy-Sobolev spaces of holomorphic functions.”

Maximal and area integral characterizations of Hardy-Soboley spaces in the unit ball of C.

Patrick Ahern, Joaquim Bruna (1988)

Revista Matemática Iberoamericana

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In this paper we deal with several characterizations of the Hardy-Sobolev spaces in the unit ball of C, that is, spaces of holomorphic functions in the ball whose derivatives up to a certain order belong to the classical Hardy spaces. Some of our characterizations are in terms of maximal functions, area functions or Littlewood-Paley functions involving only complex-tangential derivatives. A special case of our results is a characterization of H itself involving only complex-tangential...

Behavior of holomorphic functions in complex tangential directions in a domain of finite type in C.

Sandrine Grellier (1992)

Publicacions Matemàtiques

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Let Ω be a domain in C. It is known that a holomorphic function on Ω behaves better in complex tangential directions. When Ω is of finite type, the best possible improvement is quantified at each point by the distance to the boundary in the complex tangential directions (see the papers on the geometry of finite type domains of Catlin, Nagel-Stein and Wainger for precise definition). We show that this improvement is characteristic: for a holomorphic function, a regularity in complex tangential...

Division and extension in weighted Bergman-Sobolev spaces.

Joaquín M. Ortega, Joan Fàbrega (1992)

Publicacions Matemàtiques

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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...

On Hardy spaces in complex ellipsoids

Thomas Hansson (1999)

Annales de l'institut Fourier

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This paper deals with atomic decomposition and factorization of functions in the holomorphic Hardy space H 1 . Such representation theorems have been proved for strictly pseudoconvex domains. The atomic decomposition has also been proved for convex domains of finite type. Here the Hardy space was defined with respect to the ordinary Euclidean surface measure on the boundary. But for domains of finite type, it is natural to define H 1 with respect to a certain measure that degenerates near...