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Integral representations for Riesz systems in the unit ball and some applications


Author: Ashot Djrbashian
Journal: Proc. Amer. Math. Soc. 117 (1993), 395-403
MSC: Primary 42B99; Secondary 31B10, 46E15
MathSciNet review: 1116256
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Abstract: We introduce $ A_\alpha ^p$ spaces of systems of harmonic functions satisfying Cauchy-Riemann equations in $ {{\mathbf{R}}^{\mathbf{n}}}$ and find integral representations. Using these representations and estimates for the integral kernel we prove boundedness of the representation operator in $ {L^p}$ and Lipschitz classes.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1116256-2
Keywords: Riesz systems, $ A_\alpha ^p$ spaces, bounded projections, Lipschitz classes
Article copyright: © Copyright 1993 American Mathematical Society