This article is cited in 5 papers

The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function. II. The Complex Plane

T. Yu. Baiguskarov, B. N. Khabibullin, A. V. Khasanova

Bashkir State University, Ufa

Abstract: Let $u\not\equiv-\infty$ be a subharmonic function in the complex plane. We establish necessary and/or sufficient conditions for the existence of a nonzero entire function $f$ for which the modulus of the product of each of its $k$th derivative $k=0,1,\dots$, by any polynomial $p$ is not greater than the function $Ce^u$ in the entire complex plane, where $C$ is a constant depending on $k$ and $p$. The results obtained significantly strengthen and develop a number of results of Lars Hörmander (1997).

Keywords: entire function, subharmonic function, integral mean, Riesz measure, counting function.

UDC: 517.53+517.574

Received: 11.03.2016
Revised: 14.06.2016

DOI: 10.4213/mzm11155

 English version: Mathematical Notes, 2017, 101:4, 590–607

Bibliographic databases:

• 
• 
• 
•