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Vladikavkaz. Mat. Zh., 2013, Volume 15, Number 3, Pages 7–18 (Mi vmj467)  

On division problem in nonradial weighted spaces of entire functions

D. A. Abaninaab, A. V. Kuzminovab

a 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.

Full text: PDF file (191 kB)
References: PDF file   HTML file
UDC: 517.547
Received: 19.10.2012

Citation: D. A. Abanina, A. V. Kuzminova, “On division problem in nonradial weighted spaces of entire functions”, Vladikavkaz. Mat. Zh., 15:3 (2013), 7–18

Citation in format AMSBIB
\Bibitem{PolKuz13}
\by D.~A.~Abanina, A.~V.~Kuzminova
\paper On division problem in nonradial weighted spaces of entire functions
\jour Vladikavkaz. Mat. Zh.
\yr 2013
\vol 15
\issue 3
\pages 7--18
\mathnet{http://mi.mathnet.ru/vmj467}


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