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Various Types of Convergence of Sequences of Subharmonic Functions
Van Quynh Nguyen V. N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 61077, Ukraine
Abstract:
Let $\upsilon_n(x)$ be a sequence of subharmonic functions in a domain $G\subset\mathbb{R}^m$. The conditions under which the convergence of $\upsilon_n(x)$, as a sequence of generalized functions, implies its convergence in the Lebesgue spaces $L_p(\gamma)$ are studied. The results similar to ours have been obtained earlier by Hörmander and also by Ghisin and Chouigui. Hörmander investigated the case where the measure $\gamma$ is some restriction of the $m$-dimensional Lebesgue measure. Grishin and Chouigui considered the case $m=2$. In this paper we consider the case $m>2$ and general measures $\gamma$.
Key words and phrases:
subharmonic function, Radon measure.
Received: 29.10.2013 Revised: 29.09.2014
Citation:
Van Quynh Nguyen, “Various Types of Convergence of Sequences of Subharmonic Functions”, Zh. Mat. Fiz. Anal. Geom., 11:1 (2015), 63–74
Linking options:
https://www.mathnet.ru/eng/jmag610 https://www.mathnet.ru/eng/jmag/v11/i1/p63
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Abstract page: | 185 | Full-text PDF : | 125 | References: | 41 |
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