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1999 | 137 | 1 | 49-60
Tytuł artykułu

On Bell's duality theorem for harmonic functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Define $h^∞(E)$ as the subspace of $C^∞(B̅L,E)$ consisting of all harmonic functions in B, where B is the ball in the n-dimensional Euclidean space and E is any Banach space. Consider also the space $h^{-∞}(E*)$ consisting of all harmonic E*-valued functions g such that $(1-|x|)^mf$ is bounded for some m>0. Then the dual $h^∞(E*)$ is represented by $h^{-∞}(E*)$ through $⟨f,g⟩_0= lim_{r→1}ʃ_B ⟨f(rx),g(x)⟩dx$, $f ∈ h^{-∞}(E*),g ∈ h^∞(E)$. This extends the results of S. Bell in the scalar case.
Słowa kluczowe
Czasopismo
Rocznik
Tom
137
Numer
1
Strony
49-60
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-06-12
Twórcy
  • Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, C/Vera 14, Valencia 46071, Spain, jmotos@mat.upv.es
  • Instituto de Matemáticas, Universidad Nacional Autónoma de México, Unidad Cuernavaca, A. P. 273-3 Admón. 3, Cuernavaca, Morelos, 62251, México, salvador@matcuer.unam.mx
Bibliografia
  • [1] R. A. Adams, Sobolev Spaces, Academic Press, 1975.
  • [2] S. Bell, A duality theorem for harmonic functions, Michigan Math. J. 29 (1982), 123-128.
  • [3] O. Blasco, Boundary values of vector-valued harmonic functions considered as operators, Studia Math. 86 (1987), 19-33.
  • [4] O. Blasco, Boundary values of functions in vector-valued Hardy spaces and geometry on Banach spaces, J. Funct. Anal. 78 (1988), 346-364.
  • [5] O. Blasco and S. Pérez-Esteva, $L^p$ continuity of projectors of weighted harmonic Bergman spaces, preprint.
  • [6] R. Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in $L^p$, Astérisque 77 (1980), 11-66.
  • [7] J. Diestel and J. J. Uhl, Vector Measures, Amer. Math. Soc., 1977.
  • [8] J. Dieudonné, Foundations of Modern Analysis, Academic Press, New York, 1960.
  • [9] N. Dinculeanu, Vector Measures, Pergamon Press, New York, 1967.
  • [10] A. E. Djrbashian and F. A. Shamoian, Topics in the Theory of $A_α^p$ Spaces, Teubner-Texte zur Math., 1988.
  • [11] A. Grothendieck, Produits tensoriels et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
  • [12] G. Köthe, Topological Vector Spaces I, II, Springer, Heidelberg, 1969, 1979.
  • [13] E. Ligocka, The Sobolev spaces of harmonic functions, Studia Math. 84 (1986), 79-87.
  • [14] E. Ligocka, Estimates in Sobolev norms $∥·∥_p^s$ for harmonic and holomorphic functions and interpolation between Sobolev and Hölder spaces of harmonic functions, ibid. 86 (1987), 255-271.
  • [15] E. Ligocka, On the space of Bloch harmonic functions and interpolation of spaces of harmonic and holomorphic functions, ibid. 87 (1987), 223-238.
  • [16] S. Pérez-Esteva, Duality on vector-valued weighted harmonic Bergman spaces, ibid. 118 (1996), 37-47.
  • [17] E. Straube, Harmonic and analytic functions admitting a distribution boundary value, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 11 (1984), 559-591.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv137i1p49bwm
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