Authors: Avetisyan, Karen
Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Equivalent conditions for bergman space and littlewood-paley type inequalities
Journal: Journal of Computational Analysis and Applications
Volume: 9
First page: 15
Last page: 28
Issue Date: 1-Jan-2007
Rank: M23
ISSN: 1521-1398
In this paper we show that the following integrals ∫B |f(z)p(1 - |z|)αdV(z), ∫B |f(z)| p-q|∇ f(z)|q(1 - |z|)α+qdV(z), and ∫B |f(z)|p-q|R f(z)|q(1 -|z|) α+qdV(z), where p > 0, q ∈ [0, p], α ∈ (-1, ∞), and where f is a holomorphic function on the unit ball B in ℂn are comparable. This result confirms a conjecture proposed by the second author at several meetings, for example, at the International twoday meeting on complex, harmonic, and functional analysis and applications, Thessaloniki, December 12 and 13, 2003. Also we generalize the well-known inequality of Littlewood-Paley in the unit ball.
Keywords: Bergman space | Holomorphic function | Integral means | Littlewood-Paley inequality | Unit ball
Publisher: Edoxus Press

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