Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(3): 1035-1046

Printed May 31, 2015

https://doi.org/10.4134/BKMS.2015.52.3.1035

Copyright © The Korean Mathematical Society.

Hardy space of Lommel functions

Nihat Ya\u{g}mur

Erzincan University

Abstract

In this work we present some geometric properties (like starlikeness and convexity of order $\alpha $ and also close-to-convexity of order $(1+\alpha )/2$) for normalized of Lommel functions of the first kind. In order to prove our main results, we use the technique of differential subordinations and some inequalities. Furthermore, we present some applications of convexity involving Lommel functions associated with the Hardy space of analytic functions, i.e., we obtain conditions for the function $h_{\mu ,v}(z) $ to belong to the Hardy space $\mathcal{H}^{p}.$

Keywords: analytic function, Lommel functions, Hardy space

MSC numbers: Primary 30C45; Secondary 33C10