Taiwanese Journal of Mathematics

COMPLEX DIFFERENTIAL EQUATIONS WITH SOLUTIONS IN THE HARDY SPACES

Li-peng Xiao

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Abstract

In this paper, sufficient conditions for the analytic coefficients of the differential equation \[ (f^{(k)})^{n_k}+A_{k-1}(f^{(k-1)})^{n_{k-1}}+\cdots+A_1(f')^{n_1}+A_0f=0 \] are found such that all analytic solutions belong to a given $H_p^\infty-$ space, or to the Hardy space $H^p.$ The results we obtain are a generalization of some earlier results by Heittokangas, Korhonen and Rättyä.

Article information

Source
Taiwanese J. Math., Volume 18, Number 3 (2014), 909-923.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706448

Digital Object Identifier
doi:10.11650/tjm.18.2014.3705

Mathematical Reviews number (MathSciNet)
MR3213394

Zentralblatt MATH identifier
1357.34137

Subjects
Primary: 34M10: Oscillation, growth of solutions
Secondary: 30D50 30D55

Keywords
differential equation Hardy space Dirichlet-type space unit disc

Citation

Xiao, Li-peng. COMPLEX DIFFERENTIAL EQUATIONS WITH SOLUTIONS IN THE HARDY SPACES. Taiwanese J. Math. 18 (2014), no. 3, 909--923. doi:10.11650/tjm.18.2014.3705. https://projecteuclid.org/euclid.twjm/1499706448


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