On division problem in nonradial weighted spaces of entire functions

Abanina D. A. , Kuzminova A. V.
Vladikavkaz Mathematical Journal 2013. Vol. 15. Issue 3.

Abstract:
We study the inductive weighted space\(H_{u,v}^{1,\infty}\)of entire functions defined by a sequence of nonradial two-part weights \(\{q_n u(|z|)+nv(|Im z|)\}_{n=1}^\infty\), \(0<q_n\uparrow1\). Under an additional assumption on the function \(v\), we establish the division theorem in \(H_{u,v}^{1,\infty}\). We also obtain some results about sweepping out the masses of the subharmonic function \(v(|Im z|)\).

Keywords: spaces of entire function, division theorem, subharmonic function

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