Mixed-norm spaces and interpolation

Ortega, Joaquín; Fàbrega, Joan

Studia Mathematica, Tome 108 (1994), p. 233-254 / Harvested from The Polish Digital Mathematics Library

Résumé

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

Publié le : 1994-01-01

Zbl 0826.32003

EUDML-ID : urn:eudml:doc:216072

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     author = {Joaqu\'\i n Ortega and Joan F\`abrega},
     title = {Mixed-norm spaces and interpolation},
     journal = {Studia Mathematica},
     volume = {108},
     year = {1994},
     pages = {233-254},
     zbl = {0826.32003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv109i3p233bwm}
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Ortega, Joaquín; Fàbrega, Joan. Mixed-norm spaces and interpolation. Studia Mathematica, Tome 108 (1994) pp. 233-254. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv109i3p233bwm/

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