Distance Formulas on Weighted Banach Spaces of Analytic Functions

被引：0
作者：
José Bonet
Wolfgang Lusky
Jari Taskinen
机构：
[1] Universitat Politècnica de València,Instituto Universitario de Matemática Pura y Aplicada IUMPA
[2] Universität Paderborn,Institut für Mathematik
[3] University of Helsinki,Department of Mathematics and Statistics
来源：
Complex Analysis and Operator Theory | 2019年 / 13卷
关键词：
Banach spaces of analytic functions; Weight; Distance; Bloch functions; Primary 46E15; Secondary 30D45;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let v be a radial weight function on the unit disc or on the complex plane. It is shown that for each analytic function f0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_0$$\end{document} in the Banach space Hv∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_v^\infty $$\end{document} of all analytic functions f such that v|f| is bounded, the distance of f0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_0$$\end{document} to the subspace Hv0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_v^0$$\end{document} of Hv∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_v^\infty $$\end{document} of all the functions g such that v|g| vanishes at infinity is attained at a function g0∈Hv0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_0 \in H_v^0$$\end{document}. Moreover a simple, direct proof of the formula of the distance of f to Hv0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_v^0$$\end{document} due to Perfekt is presented. As a consequence the corresponding results for weighted Bloch spaces are obtained.
引用
收藏
页码：893 / 900
页数：7
相关论文
共 20 条
  • [1] Axler S(1979)Approximation by compact operators and the space Ann. Math. 109 601-612
  • [2] Berg ID(1993)Weighted spaces of holomorphic functions on bounded domains Mich. Math. J. 40 271-297
  • [3] Jewell N(1998)Associated weights and spaces of holomorphic functions Studia Math. 127 137-168
  • [4] Shields A(1975)Approximation from the space of compact operators and other M-ideals Duke Math. J. 42 259-269
  • [5] Bierstedt KD(2000)On the Fourier series of unbounded harmonic functions J. Lond. Math. Soc. 2 568-580
  • [6] Bonet J(2006)On the isomorphism classes of weighted spaces of harmonic and holomorphic functions Studia Math. 175 19-45
  • [7] Galbis A(2013)Duality and distance formulas in spaces defined by means of oscillation Ark. Mat. 51 345-361
  • [8] Bierstedt KD(2017)On M-ideals and o–O type spaces Math. Scand. 121 151-160
  • [9] Bonet J(1971)Bounded projections, duality and multipliers in spaces of analytic functions Trans. Am. Math. Soc. 162 287-302
  • [10] Taskinen J(2006)Distance of a Bloch function to the little Bloch space Bull. Aust. Math. Soc. 74 101-119
12