Hardy Space of Lommel Functions

In this work we present some geometric properties (like star-likeness and convexity of order <TEX>α</TEX> and also close-to-convexity of order (<TEX>1+α</TEX>)/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 <TEX>h_μ,υ(z)</TEX> to belong to the Hardy space <TEX>Hᵖ</TEX>.