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Holomorphic liftings and Bergman kernel estimates for ℱ-domains

✍ Scribed by Wolfram Bauer

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
284 KB
Volume
281
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let E be a 𝒟ℱ𝒩‐space and let U ⊂ E be open. By applying the nuclearity of the Fréchet space ℋ︁(U) of holomorphic functions on U we show that there are finite measures μ on U leading to Bergman spaces of μ ‐square integrable holomorphic functions. We give an explicit construction for μ by using infinite dimensional Gaussian measures. Moreover, we prove boundary estimates for the corresponding Bergman kernels K~μ~ on the diagonal and we give an application of our results to liftings of μ ‐square integrable Banach space valued holomorphic functions over U. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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