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Ufimsk. Mat. Zh., 2011, Volume 3, Issue 4, Pages 86–94 (Mi ufa120)  

The indicator of a delta-subharmonic function in a half-plane

K. G. Malyutina, N. Sadikb

a Sumy State University, Sumy, Ukraine
b Istanbul University, Fen Fakultesi, Matematik Bolumu, Istanbul, Turkey

Abstract: Delta-subharmonic functions of a completely regular growth in the upper half-plane have been introduced in the joint work of the authors, published in Reports of the Russian Academy of Sciences (2001). In this work, criteria whether a delta-subharmonic function in the upper half-plane belongs to a class of functions of a completely regular growth have been obtained on the basis of the theory of Fourier coefficients of delta-subharmonic functions in the half-plane developed in the beginning of this century by the first author of the present article. The present paper is a natural continuation of this research. The concept of the indicator of a delta-subharmonic function of a completely regular growth in the upper half-plane is introduced. It is proved that the indicator of a delta-subharmonic function of a completely regular growth in the upper half-plane belongs to a class $L_p[0,\pi]$ ($1<p\leq2$). The proof is based on the lemma about Polya peaks and the Hausdorff–Young theorem.

Keywords: delta-subharmonic functions of a completely regular growth in the upper half-plane, Fourier coefficients, the indicator, Polya peaks, Hausdorff–Young theorem.

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Bibliographic databases:

Document Type: Article
UDC: 517.9
Received: 10.06.2011

Citation: K. G. Malyutin, N. Sadik, “The indicator of a delta-subharmonic function in a half-plane”, Ufimsk. Mat. Zh., 3:4 (2011), 86–94

Citation in format AMSBIB
\Bibitem{MalSad11}
\by K.~G.~Malyutin, N.~Sadik
\paper The indicator of a~delta-subharmonic function in a~half-plane
\jour Ufimsk. Mat. Zh.
\yr 2011
\vol 3
\issue 4
\pages 86--94
\mathnet{http://mi.mathnet.ru/ufa120}
\zmath{https://zbmath.org/?q=an:1249.30096}


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