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Displaying similar documents to “On some spaces of holomorphic functions of exponential growth on a half-plane”

Hölder functions in Bergman type spaces

Yingwei Chen, Guangbin Ren (2012)

Studia Mathematica

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It seems impossible to extend the boundary value theory of Hardy spaces to Bergman spaces since there is no boundary value for a function in a Bergman space in general. In this article we provide a new idea to show what is the correct version of Bergman spaces by demonstrating the extension to Bergman spaces of a result of Hardy-Littlewood in Hardy spaces, which characterizes the Hölder class of boundary values for a function from Hardy spaces in the unit disc in terms of the growth...

Weighted Bergman projections and tangential area integrals

William Cohn (1993)

Studia Mathematica

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Let Ω be a bounded strictly pseudoconvex domain in ℂ n . In this paper we find sufficient conditions on a function f defined on Ω in order that the weighted Bergman projection P s f belong to the Hardy-Sobolev space H k p ( ∂ Ω ) . The conditions on f we consider are formulated in terms of tent spaces and complex tangential vector fields. If f is holomorphic then these conditions are necessary and sufficient in order that f belong to the Hardy-Sobolev space H k p ( ∂ Ω ) .

Three related problems of Bergman spaces of tube domains over symmetric cones

Aline Bonami (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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It has been known for a long time that the Szegö projection of tube domains over irreducible symmetric cones is unbounded in L p for p ≠ 2 . Indeed, this is a consequence of the fact that the characteristic function of a disc is not a Fourier multiplier, a fundamental theorem proved by C. Fefferman in the 70’s. The same problem, related to the Bergman projection, deserves a different approach. In this survey, based on joint work of the author with D. Békollé, G. Garrigós, M. Peloso and F. Ricci,...

Bergman function, Genchev transform and L²-angles, for multidimensional tubes

Hyb Wojciech

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CONTENTS1. Introduction.......................................................................................................52. Basic definitions, notations and facts................................................................63. Definitions of the Genchev transform................................................................84. Basic properties of the Genchev transform......................................................115. Some properties of the weight w B ..............................................................166....

Bloch type spaces on the unit ball of a Hilbert space

Zhenghua Xu (2019)

Czechoslovak Mathematical Journal

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We initiate the study of Bloch type spaces on the unit ball of a Hilbert space. As applications, the Hardy-Littlewood theorem in infinite-dimensional Hilbert spaces and characterizations of some holomorphic function spaces related to the Bloch type space are presented.

Holomorphic Sobolev spaces on the ball

Frank Beatrous, Jacob Burbea

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CONTENTSIntroduction ..............................................................50. Preliminaries and notation....................................61. Hilbert spaces of holomorphic functions..............112. Some estimates ..................................................163. The space L q p ............................................224. Norm estimates...................................................305. Sobolev norms....................................................356. Projections...