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References (27)
-
J. Heittokangas (2005)
Solutions of f″ + A(z)f = 0 in the Unit Disc Having Blaschke Sequences as the ZerosComputational Methods and Function Theory, 5
-
J. Heittokangas, I. Laine (2005)
SOLUTIONS OF f 00 + A(z)f = 0 WITH PRESCRIBED SEQUENCES OF ZEROS -
J. Earl (1970)
On the Interpolation of Bounded Sequences by Bounded FunctionsJournal of The London Mathematical Society-second Series, 2
-
J. Rättyä (2003)
n-th derivative characterisations, mean growth of derivatives and F(p, q, s)Bulletin of the Australian Mathematical Society, 68
-
R. Zhao (2008)
DISTANCES FROM BLOCH FUNCTIONS TO SOME MÖBIUS INVARIANT SPACES, 33
-
Cheng Yuan, C. Tong (2018)
On Analytic Campanato and F(p, q, s) SpacesComplex Analysis and Operator Theory, 12
-
(2001)
HolomorphicQ Classes, LNM 1767 -
R. Aulaskari, J. Xiao, R. Zhao (1995)
ON SUBSPACES AND SUBSETS OF BMOA AND UBC, 15
-
J. Heittokangas (2013)
A Survey on Blaschke-Oscillatory Differential Equations, with Updates -
J. Gröhn (2017)
Solutions of Complex Differential Equation Having Pre-given Zeros in the Unit DiscConstructive Approximation, 49
-
J. Ortega, J. Fàbrega (1996)
Pointwise multipliers and corona type decomposition in $BMOA$Annales de l'Institut Fourier, 46
-
P. Duren (1970)
Theory of H[p] spaces -
A. Nicolau, J. Xiao (1997)
Bounded Functions in Mo bius Invariant Dirichlet Spaces -
F. Pérez-González, J. Rättyä (2009)
Inner functions in the Möbius invariant Besov-type spacesProceedings of the Edinburgh Mathematical Society, 52
-
Z. Nehari (1950)
Bounded analytic functionsBulletin of the American Mathematical Society, 57
-
Kehe Zhu (1990)
Operator theory in function spaces -
G. Bao, Jordi Pau (2015)
Boundary multipliers of a family of M\"obius invariant function spacesarXiv: Complex Variables
-
(1997)
Some results onQp spaces, 0 -
L. Carleson (1958)
An Interpolation Problem for Bounded Analytic FunctionsAmerican Journal of Mathematics, 80
-
J. Peetre, J. Arazy, S. Fisher (1985)
Möbius invariant function spaces.Journal für die reine und angewandte Mathematik (Crelles Journal), 1985
-
J. Heittokangas, Atte Reijonen (2014)
ON THE COMPLEXITY OF FINDING A NECESSARY AND SUFFICIENT CONDITION FOR BLASCHKE-OSCILLATORY EQUATIONSGlasgow Mathematical Journal, 57
-
J. Gröhn, J. Heittokangas (2012)
New Findings on the Bank–Sauer Approach in Oscillation TheoryConstructive Approximation, 35
-
(2001)
On some complex function spaces and classes -
A. Kerr-Lawson (1969)
Some Lemmas on Interpolating Blaschke Products and a CorrectionCanadian Journal of Mathematics, 21
-
M. Bakhit (2016)
Closed Range Composition Operators on a General Family of Function SpacesAnalysis in Theory and Applications, 32
-
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations -
J. Xiao (2006)
Geometric Qp Functions
- Publisher
- Springer Journals
- Copyright
- Copyright © Springer-Verlag GmbH Germany, part of Springer Nature 2020
- ISSN
- 1617-9447
- eISSN
- 2195-3724
- DOI
- 10.1007/s40315-020-00318-9
- Publisher site
- See Article on Publisher Site
Abstract
For 0<s<1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0<s<1$$\end{document}, let Λ⊂D\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Lambda \subset {\mathbb {D}}$$\end{document} be a separated sequence such that ∑zn∈Λ(1-|zn|)sδzn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\sum _{z_n\in \Lambda }(1-|z_n|)^s \delta _{z_n}$$\end{document} is an s-Carleson measure. In this paper, we show that there exist certain analytic functions A such that the second order complex differential equation f′′+Af=0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$f''+Af=0$$\end{document} admits a non-trivial solution f whose zero-sequence is Λ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Lambda $$\end{document}, where the solution f belongs to some Möbius invariant function spaces. We strengthen a previous result from the literature.
Journal
Computational Methods and Function Theory – Springer Journals
Published: May 11, 2020