2019
Том 71
№ 11

All Issues

Kondratyuk Ya. V.

Articles: 7
Brief Communications (Russian)

On the Growth of Infinite-Order Subharmonic Functions in ℂ

Kondratyuk Ya. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 9. - pp. 1276-1281

For infinite-order functions u subharmonic in \(\mathbb{C}\) with given restrictions on the Riesz masses of a disk of radius r ∈ (0, +∞), we find majorants for the functions \(B\left( {r,u} \right) = \max \left\{ {\left| {u\left( z \right)} \right|:\left| z \right| \leqslant r} \right\}\) and \(\overset{\lower0.5em\hbox{\(\smash{\scriptscriptstyle\smile}\)}}{B} \left( {r,u} \right) = \sup \left\{ {\left| {\overset{\lower0.5em\hbox{\(\smash{\scriptscriptstyle\smile}\)}}{u} \left( z \right)} \right|:\left| z \right| \leqslant r} \right\}\) , where \(\overset{\lower0.5em\hbox{\(\smash{\scriptscriptstyle\smile}\)}}{u}\) is a function conjugate to u.

Brief Communications (Ukrainian)

Generalized Lindelöf Finiteness Conditions for the λ-Type of a Subharmonic Function

Kondratyuk A. A., Kondratyuk Ya. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 2. - pp. 276-179

We establish a finiteness criterion for the λ-type of a subharmonic function. In the case where λ(r) = r ρ L(r), ρ, where L is a slowly varying function, this criterion coincides with the Lindelöf criterion.

Article (Ukrainian)

On the boundedness of the total variation of the logarithm of a Blaschke product

Kondratyuk Ya. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 11. - pp. 1449–1455

We establish that, for a Blaschke product B(z) convergent in the unit disk, the condition - ∞ < \(\smallint _0^1 \log (1 - t)n(t,B)dt\) is sufficient for the total variation of logB to be bounded on a circle of radiusr, 0 <r < 1. For products B(z) with zeros concentrated on a single ray, this condition is also necessary. Here, n(t, B) denotes the number of zeros of the functionB (z) in a disk of radiust.

Brief Communications (Ukrainian)

On boundedness of square means for the logarithms of Blaschke products

Kondratyuk A. A., Kondratyuk Ya. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 2. - pp. 255–259

We establish conditions for boundedness of square means of the logarithms of Blaschke products.

Article (Ukrainian)

General páley problem

Kondratyuk A. A., Kondratyuk Ya. V., Tarasyuk S. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 1. - pp. 25-34

In the class of functions u of finite lower order subharmonic in ℝ p+2,p ∈ ℕ we establish an exact upper bound for $$\mathop {\lim }\limits_{r \to \infty } \inf \frac{{m_q (r,u^ + )}}{{T(r,u)}}, 1< q \le \infty ,$$ whereT(r, u) is a Nevanlinna characteristic of the function u andm q (r, u +) is the integralq-mean of the functionu +,u + = max(u,0), on the sphere of radiusr.

Article (Ukrainian)

A Criterion for the completely regular growth of δ-subharmonic functions

Kondratyuk Ya. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1985. - 37, № 1. - pp. 8 – 13

Article (Ukrainian)

Asymptotic behavior of in |f ( r e i θ )| in the L q [0; 2π]-norm in a class of entire functions

Kondratyuk A. A., Kondratyuk Ya. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1982. - 34, № 1. - pp. 1-8