On generalized Bergman spaces

Wolfgang Lusky

Studia Mathematica (1996)

  • Volume: 119, Issue: 1, page 77-95
  • ISSN: 0039-3223

Abstract

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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 2 π | f ( r e i φ ) | p d φ ) q / p d μ ( r ) < ∞ .

How to cite

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Lusky, Wolfgang. "On generalized Bergman spaces." Studia Mathematica 119.1 (1996): 77-95. <http://eudml.org/doc/216287>.

@article{Lusky1996,
abstract = {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 $ʃ_\{0\}^\{1\} (ʃ_\{0\}^\{2π\} |f(re^\{iφ\})|^p dφ)^\{q/p\} dμ(r) < ∞$.},
author = {Lusky, Wolfgang},
journal = {Studia Mathematica},
keywords = {open unit disc; positive bounded measure; Banach-space descriptions of the classes of all harmonic (holomorphic) functions},
language = {eng},
number = {1},
pages = {77-95},
title = {On generalized Bergman spaces},
url = {http://eudml.org/doc/216287},
volume = {119},
year = {1996},
}

TY - JOUR
AU - Lusky, Wolfgang
TI - On generalized Bergman spaces
JO - Studia Mathematica
PY - 1996
VL - 119
IS - 1
SP - 77
EP - 95
AB - 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 $ʃ_{0}^{1} (ʃ_{0}^{2π} |f(re^{iφ})|^p dφ)^{q/p} dμ(r) < ∞$.
LA - eng
KW - open unit disc; positive bounded measure; Banach-space descriptions of the classes of all harmonic (holomorphic) functions
UR - http://eudml.org/doc/216287
ER -

References

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  1. [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. [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. Zbl0801.46021
  3. [3] O. Blasco, Multipliers on weighted Besov spaces of analytic functions, in: Contemp. Math. 144, Amer. Math. Soc., 1993, 23-33. Zbl0838.42002
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  13. [13] M. Mateljević and M. Pavlović, L p -behaviour of the integral means of analytic functions, Studia Math. 77 (1984), 219-237. 
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  17. [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. Zbl0508.31001
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  20. [20] P. Wojtaszczyk, On unconditional polynomial bases in L p and Bergman spaces, Constr. Approx., to appear. Zbl0863.41004

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