# Article

Ufa Mathematical Journal
Volume 3, Number 4, pp. 84-91

# An indicator of a delta-subharmonic function in the half-plane

Delta-subharmonic functions of completely regular growth in a upper half-plane have been entered in the teamwork of authors published in Reports of the Russian Academy of Sciences (2001). In this work, leaning on 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 this article, have been received criteria that a delta-subharmonic in the upper half-plane function belongs to a class completely regular growth in a upper half-plane. The present work is natural continuation of these researches. In work the concept of the indicator delta-subharmonic function of completely regular growth in a top half-plane is entered. It is proved that the indicator of the delta-subharmonic function of completely regular growth in a upper half-plane belongs to a class $L_p [0, \pi]$ (\$1