Mixed-norm spaces and interpolation

• Autorzy: Joaquín M. Ortega , Joan Fàbrega
• 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.

Słowa kluczowe

EN

analytic functions; mixed-norm spaces; real interpolation; complex interpolation; Besov spaces of holomorphic functions

Kategorie tematyczne

• 32A99: None of the above, but in this section
• 32A10: Holomorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 109
• Numer: 3
• Strony: 233-254

Daty

wydano

1994

otrzymano

1993-01-26

poprawiono

1993-09-13

Twórcy

autor

Joaquín M. Ortega

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

autor

Joan Fàbrega

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

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