Holomorphic liftings and Bergman kernel estimates for 𝒟ℱ𝒩‐domains | Zendy

Bauer Wolfram | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

Holomorphic liftings and Bergman kernel estimates for 𝒟ℱ𝒩‐domains

Author(s) -

Bauer Wolfram

Publication year - 2008

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200610640

Subject(s) - holomorphic function , mathematics , square integrable function , bergman kernel , bergman space , pure mathematics , banach space , diagonal , boundary (topology) , space (punctuation) , integrable system , identity theorem , kernel (algebra) , square (algebra) , mathematical analysis , geometry , bounded function , linguistics , philosophy

Let E be a ℱ‐space and let U ⊂ E be open. By applying the nuclearity of the Fréchet space ℋ( 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)

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research