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Czasopismo
1994 | 109 | 3 | 233-254
Tytuł artykułu

Mixed-norm spaces and interpolation

Treść / Zawartość
Warianty tytułu
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
Opis fizyczny
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., ortega@cerber.ub.es
  • Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, E-08071 Barcelona, Spain., fabrega@cerber.ub.es
Bibliografia
  • [AM] E. Amar, Suites d'interpolation pour les classes de Bergman de la boule et du polydisque de $ℂ^n$, Canad. J. Math. 30 (1978), 711-737.
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  • [BEA-BU] F. Beatrous and J. Burbea, Sobolev spaces of holomorphic functions in the ball, Dissertationes Math. 276 (1989).
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  • [BR-OR2] J. Bruna and J. M. Ortega, Interpolation in Hardy-Sobolev spaces, preprint.
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  • [CO-WE] R. Coifman et G. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math. 242, Springer, Berlin, 1971.
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  • [DU] P. Duren, Theory of $H^p$ Spaces, Academic Press, New York, 1970.
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  • [GA] S. Gadbois, Mixed-norm generalizations of Bergman spaces and duality, Proc. Amer. Math. Soc. 104 (1988), 1171-1180.
  • [HA-LIT] G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals II, Math. Z. 28 (1932), 612-634.
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  • [LI2] E. Ligocka, On duality and interpolation for spaces of polyharmonic functions, ibid. 88 (1988), 139-163.
  • [LU] D. H. Luecking, Representation and duality in weighted spaces of analytic functions, Indiana Univ. Math. J. 34 (1985), 319-336.
  • [OR] J. M. Ortega, The Gleason problem in Bergman-Sobolev spaces, Complex Variables 20 (1992), 157-170.
  • [OR-FA] J. M. Ortega and J. Fàbrega, Division and extension in weighted Bergman-Sobolev spaces, Publ. Mat. 36 (1992), 837-859.
  • [RO] R. Rochberg, Interpolation by functions in Bergman spaces, Michigan Math. J. 29 (1982), 229-236.
  • [SH] J. H. Shi, Inequalities for the integral means of holomorphic functions and their derivatives in the unit ball of $ℂ^n$, Trans. Amer. Math. Soc. 328 (1991), 619-637.
  • [ST] E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.
  • [STR] E. Straube, Interpolation between Sobolev and between Lipschitz spaces of analytic functions on starshaped domains, Trans. Amer. Math. Soc. 316 (1989), 653-671.
  • [TR1] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
  • [TR2] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, 1983.
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv109i3p233bwm
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