On division problem in nonradial weighted spaces of entire functions

D. A. Abanina^ab, A. V. Kuzminova<sup>b

a</sup> Southern Federal University, Rostov-on-Don, Russia
^b South Mathematical Institute of VSC RAS, Vladikavkaz, Russia

Abstract: We study the inductive weighted space $H_{u,v}^{1,\infty}$ of entire functions defined by a sequence of nonradial two-part weights $\{q_nu(|z|)+nv(|\operatorname{Im}z|)\}_{n=1}^\infty$, $0<q_n\uparrow1$. 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 $v(|\operatorname{Im}z|)$.

Key words: spaces of entire function, division theorem, subharmonic function.

UDC: 517.547

Received: 19.10.2012