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Czasopismo

1994 | 109 | 3 | 233-254

Tytuł artykułu

Mixed-norm spaces and interpolation

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
Let D be a bounded strictly pseudoconvex domain of $ℂ^n$ with smooth boundary. We consider the weighted mixed-norm spaces $A^{p,q}_{δ,k}(D)$ of holomorphic functions with norm $∥f∥_{p,q,δ,k} = (∑_{|α|≤k} ʃ_{0}^{r_0} (ʃ_{∂D_{r}} |D^{α} f|^p dσ_{r})^{q/p} r^{δq/p-1} dr)^{1/q}$. We prove that these spaces can be obtained by real interpolation between Bergman-Sobolev spaces $A^{p}_{δ,k}(D)$ and we give results about real and complex interpolation between them. We apply these results to prove that $A^{p,q}_{δ,k}(D)$ is the intersection of a Besov space $B^{p,q}_{s}(D)$ with the space of holomorphic functions on D. Further, we obtain several properties of the mixed-norm spaces.

Czasopismo

Rocznik

Tom

109

Numer

3

Strony

233-254

Daty

wydano
1994
otrzymano
1993-01-26
poprawiono
1993-09-13

Twórcy

  • Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, E-08071 Barcelona, Spain.
  • Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, E-08071 Barcelona, Spain.

Bibliografia

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