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1996 | 119 | 1 | 77-95
Tytuł artykułu

On generalized Bergman spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let D be the open unit disc and μ a positive bounded measure on [0,1]. Extending results of Mateljević/Pavlović and Shields/Williams we give Banach-space descriptions of the classes of all harmonic (holomorphic) functions f: D → ℂ satisfying $ʃ_{0}^{1} (ʃ_{0}^{2π} |f(re^{iφ})|^p dφ)^{q/p} dμ(r) < ∞$.
Słowa kluczowe
Czasopismo
Rocznik
Tom
119
Numer
1
Strony
77-95
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-09-28
poprawiono
1996-02-16
Twórcy
  • Fachbereich 17, Universität-Gesamthochschule, Warburger Straße 100, D-33098 Paderborn, Germany, lusky@uni-paderborn.de
Bibliografia
  • [1] S. Axler, Bergman spaces and their operators, in: Survey of Some Recent Results in Operator Theory, B. Conway and B. Morrel (eds.), Pitman Res. Notes, 1988, 1-50.
  • [2] K. D. Bierstedt and W. H. Summers, Biduals of weighted Banach spaces of analytic functions, J. Austral. Math. Soc. Sec. A 54 (1993), 70-79.
  • [3] O. Blasco, Multipliers on weighted Besov spaces of analytic functions, in: Contemp. Math. 144, Amer. Math. Soc., 1993, 23-33.
  • [4] R. R. Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in $L^p$, Astérisque 77 (1980), 12-66.
  • [5] P. L. Duren, Theory of $H^p$-Spaces, Academic Press, New York, 1970.
  • [6] T. M. Flett, The dual of an inequality of Hardy and Littlewood and some related inequalities, J. Math. Anal. Appl. 38 (1972), 746-765.
  • [7] T. M. Flett, Lipschitz spaces of functions on the circle and the disc, ibid. 39 (1972), 125-158.
  • [8] G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals II, Math. Z. 34 (1932), 403-439.
  • [9] G. H. Hardy and J. E. Littlewood, Theorems concerning mean values of analytic or harmonic functions, Quart. J. Math. 12 (1941), 221-256.
  • [10] J. Lindenstrauss and A. Pełczyński, Contributions to the theory of classical Banach spaces, J. Funct. Anal. 8 (1971), 225-249.
  • [11] W. Lusky, On the structure of $Hv_0(D)$ and $hv_0(D)$, Math. Nachr. 159 (1992), 279-289.
  • [12] W. Lusky, On weighted spaces of harmonic and holomorphic functions, J. London Math. Soc. (2) 51 (1995), 309-320.
  • [13] M. Mateljević and M. Pavlović, $L^p$-behaviour of the integral means of analytic functions, Studia Math. 77 (1984), 219-237.
  • [14] L. A. Rubel and A. L. Shields, The second duals of certain spaces of analytic functions, J. Austral. Math. Soc. 11 (1970), 276-280.
  • [15] A. L. Shields and D. L. Williams, Bounded projections, duality and multipliers in spaces of analytic functions, Trans. Amer. Math. Soc. 162 (1971), 287-302.
  • [16] A. L. Shields and D. L. Williams, Bounded projections, duality and multipliers in spaces of harmonic functions, J. Reine Angew. Math. 299/300 (1978), 256-279.
  • [17] A. L. Shields and D. L. Williams, Bounded projections and the growth of harmonic conjugates in the unit disc, Michigan Math. J. 29 (1982), 3-25.
  • [18] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, New York, 1986.
  • [19] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge University Press, 1991.
  • [20] P. Wojtaszczyk, On unconditional polynomial bases in $L_p$ and Bergman spaces, Constr. Approx., to appear.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv119i1p77bwm
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