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1997 | 66 | 1 | 183-201
Tytuł artykułu

A natural localization of Hardy spaces in several complex variables

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EN
Abstrakty
EN
Let H²(bΩ) be the Hardy space of a bounded weakly pseudoconvex domain in $ℂ^n$. The natural resolution of this space, provided by the tangential Cauchy-Riemann complex, is used to show that H²(bΩ) has the important localization property known as Bishop's property (β). The paper is accompanied by some applications, previously known only for Bergman spaces.
Twórcy
  • Department of Mathematics, University of California, Riverside, California 92521, U.S.A.
autor
  • Mathematisches Institut, Westfälische Wilhelms-Universität, 48149 Münster, Germany
  • Fachbereich Mathematik, Universität des Saarlandes, 6600 Saarbrücken, Germany
Bibliografia
  • [1] E. Bishop, A duality theorem for an arbitrary operator, Pacific J. Math. 9 (1959), 379-394.
  • [2] A. Boggess, CR Manifolds and the Tangential Cauchy-Riemann Complex, CRC Press, Boca Raton, Fla., 1991.
  • [3] A. Douady, Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné, Ann. Inst. Fourier (Grenoble) 16 (1) (1966), 1-95.
  • [4] R. G. Douglas and V. Paulsen, Hilbert Modules over Function Algebras, Pitman Res. Notes Math. Ser. 219, Harlow, 1989.
  • [5] R. G. Douglas, V. Paulsen, C. H. Sah, and K. Yan, Algebraic reduction and rigidity for Hilbert modules, Amer. J. Math. 117 (1995), 75-92.
  • [6] N. Dunford and J. T. Schwartz, Linear Operators, Part III, Wiley-Interscience, New York, 1971.
  • [7] J. Eschmeier and M. Putinar, Spectral Decompositions and Analytic Sheaves, London Math. Soc. Monographs, Oxford Univ. Press, Oxford, 1996.
  • [8] C. Foiaş, Spectral maximal spaces and decomposable operators in Banach space, Arch. Math. (Basel) 14 (1963), 341-349.
  • [9] G. M. Henkin, H. Lewy's equation and analysis on pseudoconvex manifolds, Russian Math. Surveys 32 (1977), 59-130 (transl. from Uspekhi Mat. Nauk 32 (3) (1977), 57-118).
  • [10] J. J. Kohn, The range of the tangential Cauchy-Riemann operator, Duke Math. J. 53 (1986), 525-545.
  • [11] S. G. Krantz, Function Theory of Several Complex Variables, Wadsworth, Belmont, Calif., 1992.
  • [12] S. G. Krantz, Partial Differential Equations and Complex Analysis, CRC Press, Boca Raton, Fla., 1992.
  • [13] M. Putinar, Quasi-similarity of tuples with Bishop's property (β), Integral Equations Operator Theory 15 (1992), 1047-1052.
  • [14] R. M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Grad. Texts in Math. 108, Springer, New York, 1986.
  • [15] M.-C. Shaw, Local solvability and estimates for $∂̅_b$ on CR manifolds, in: Proc. Sympos. Pure Math. 52, Amer. Math. Soc., Providence, R.I., 1991, 335-345.
  • [16] F. Treves, Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1967.
  • [17] F. H. Vasilescu, Analytic Functional Calculus and Spectral Decompositions, Reidel, Dordrecht, 1982.
  • [18] R. Wolff, Spectra of analytic Toeplitz tuples on Hardy spaces, Bull. London Math. Soc., to appear
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-apmv66z1p183bwm
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