Two-member asymptotics of Young conjugated functions and problems of behaviour of positive sequences

M.M.Sheremeta

Let $P$ and $Q$ be Young conjugated functions, $\Phi_1$ be a convex on $(-\|,+\|)$ positive increasing to $+\|$ function and $\Phi_2$ be positive on $(-\|,+\|)$ function such that $\Phi_2(\sigma)=o(\Phi_1(\sigma))$ $(\sigma\to+\|)$. The problem of validity of the relation $Q(\sigma)=\Phi_1(\sigma)+\tau(1+o(1))\Phi_2(\sigma)$ $(\sigma\to +\|)$, where $\tau$ is a real number, is discussed.

1. Sheremeta M. M., Fedyniak S. I. On the derivative of Dirichlet series, Sibirsk. matem. journ. 39 (1998), no.1, 206–223 (in Russian).

2. Zabolotskyi M.V., Sheremeta M.M. A generalization of Lindelöf Theorem, Ukr. matem. journ. 50 (1998), no.9, 1177–1192 (in Ukrainian).

3. Sheremeta M. M. Estimates of the maximal term of entire Dirichlet series in terms of two-member asymptotics, Matematychni Studii, 14 (2000), no.2, 159–164.

4. Sheremeta M. M., Sumyk O. M. A connection between the growth of Young conjugated functions, Matematychni studii 11 (1999), no.1, 41–47 (in Ukrainian).

	Two-member asymptotics of Young conjugated functions and problems of behaviour of positive sequences
Author	M.M.Sheremeta Faculty of Mechanics and Mathematics, Lviv National University
Abstract	Let $P$ and $Q$ be Young conjugated functions, $\Phi_1$ be a convex on $(-\\|,+\\|)$ positive increasing to $+\\|$ function and $\Phi_2$ be positive on $(-\\|,+\\|)$ function such that $\Phi_2(\sigma)=o(\Phi_1(\sigma))$ $(\sigma\to+\\|)$. The problem of validity of the relation $Q(\sigma)=\Phi_1(\sigma)+\tau(1+o(1))\Phi_2(\sigma)$ $(\sigma\to +\\|)$, where $\tau$ is a real number, is discussed.
Keywords	Young conjugate functions, convex functions, asymptotic relations, growth of functions, validity conditions
DOI	doi:10.30970/ms.14.2.217-220
Reference	1. Sheremeta M. M., Fedyniak S. I. On the derivative of Dirichlet series, Sibirsk. matem. journ. 39 (1998), no.1, 206–223 (in Russian). 2. Zabolotskyi M.V., Sheremeta M.M. A generalization of Lindelöf Theorem, Ukr. matem. journ. 50 (1998), no.9, 1177–1192 (in Ukrainian). 3. Sheremeta M. M. Estimates of the maximal term of entire Dirichlet series in terms of two-member asymptotics, Matematychni Studii, 14 (2000), no.2, 159–164. 4. Sheremeta M. M., Sumyk O. M. A connection between the growth of Young conjugated functions, Matematychni studii 11 (1999), no.1, 41–47 (in Ukrainian).
Pages	217-220
Volume	14
Issue	2
Year	2000
Journal	Matematychni Studii
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