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FAMILIES OF FRACTIONAL FANTAPPIÈ TRANSFORMS

Part of: Linear function spaces and their duals Holomorphic functions of several complex variables Commutative Banach algebras and commutative topological algebras

Published online by Cambridge University Press:  07 April 2010

EVGUENI DOUBTSOV
EVGUENI DOUBTSOV*
Affiliation:
St. Petersburg Department of V.A. Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia (email: [email protected])
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Abstract

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Let Bn denote the unit ball in ℂn, n≥1. Given an α>0, let ℱα(n) denote the class of functions defined for z∈Bn by integrating the kernel (1−〈z,w〉)−α against a complex Borel measure dμ(w), w∈Bn. The family ℱ0(n) corresponds to the logarithmic kernel log (1/(1−〈z,w〉)). Various properties of the spaces ℱα(n), α≥0, are obtained. In particular, pointwise multiplies for ℱα(n) are investigated.

Keywords

fractional Fantappiè transformpointwise multiplier

MSC classification

Secondary: 32A26: Integral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels) 46E15: Banach spaces of continuous, differentiable or analytic functions 46J15: Banach algebras of differentiable or analytic functions, $H^p$-spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 1 , August 2010 , pp. 62 - 78
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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