Interpolation d'opérateurs entre espaces de fonctions holomorphes

Patrice Lassere

Annales Polonici Mathematici (1991)

  • Volume: 56, Issue: 1, page 97-102
  • ISSN: 0066-2216

Abstract

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Let K be a compact subset of an hyperconvex open set D ⊂ ℂ n , forming with D a Runge pair and such that the extremal p.s.h. function ω(·,K,D) is continuous. Let H(D) and H(K) be the spaces of holomorphic functions respectively on D and K equipped with their usual topologies. The main result of this paper contains as a particular case the following statement: if T is a continuous linear map of H(K) into H(K) whose restriction to H(D) is continuous into H(D), then the restriction of T to H ( D α ) is a continuous linear map of H ( D α ) into H ( D α ) , ∀α ∈ ]0,1[ where D α = z ∈ D : ω ( z , D , K ) < α .

How to cite

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Patrice Lassere. "Interpolation d'opérateurs entre espaces de fonctions holomorphes." Annales Polonici Mathematici 56.1 (1991): 97-102. <http://eudml.org/doc/262327>.

@article{PatriceLassere1991,
author = {Patrice Lassere},
journal = {Annales Polonici Mathematici},
keywords = {interpolation of operators; spaces of analytic functions; common Schauder bases; holomorphic functions; interpolation},
language = {fre},
number = {1},
pages = {97-102},
title = {Interpolation d'opérateurs entre espaces de fonctions holomorphes},
url = {http://eudml.org/doc/262327},
volume = {56},
year = {1991},
}

TY - JOUR
AU - Patrice Lassere
TI - Interpolation d'opérateurs entre espaces de fonctions holomorphes
JO - Annales Polonici Mathematici
PY - 1991
VL - 56
IS - 1
SP - 97
EP - 102
LA - fre
KW - interpolation of operators; spaces of analytic functions; common Schauder bases; holomorphic functions; interpolation
UR - http://eudml.org/doc/262327
ER -

References

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  1. [B.T.] E. Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1-40. Zbl0547.32012
  2. [B] S. Bergman, The Kernel Function and Conformal Mapping, Math. Surveys 5, Amer. Math. Soc., 1970. Zbl0208.34302
  3. [L.P.] J. L. Lions et J. Peetre, Sur une classe d'espaces d'interpolation, Publ. Math. I.H.E.S. 19 (1964), 4-68. 
  4. [MA] H. Mascart, Sur quelques opérateurs linéaires différentiels, Ann. Fac. Sci. Toulouse 24 (1960), 5-73. Zbl0117.04903
  5. [N] Nguyen Thanh Van, Bases de Schauder dans certains espaces de fonctions holomorphes, Ann. Inst. Fourier (Grenoble) 22 (2) (1972), 169-253. Zbl0226.46025
  6. [ZA-1,2] V. P. Zakharyuta, Fonctions plurisousharmoniques extrémales, échelles hilbertiennes et isomorphismes d'espaces de fonctions analytiques de plusieurs variables complexes I, II, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 19 (1974), 133-157; 21 (1974), 65-83 (en russe). 
  7. [ZE] A. Zeriahi, Bases de Schauder et isomorphismes d'espaces de fonctions holomorphes, C. R. Acad. Sci. Paris 310 (1990), 691-694. Zbl0721.32002

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