arXiv subjects

Aleksandr Rotkevich

Publications and source records attributed to Aleksandr Rotkevich.

4 recordsLinked to original sources

arXiv2025

An example of a space $L^{p(\cdot)}$ on which the Cauchy-Leray-Fantappi\`{e} operator for complex ellipsoid is not bounded

We construct an example of a Lebesgue space with variable exponent on which Cauchy-Leray-Fantappi\`{e} operator associated with a complex ellipsoid is not bounded. This result extends previous counterexamples for the unit ball and demonstrates that the logarithmic continuity condition for the exponent function $p(\cdot)$ is sharp even for non-strictly convex domains. The proof is based on an explicit construction of test functions supported near points where the boundary fails to be strictly convex.

math.CV↗

arXiv2020

Constructive description of Hardy-Sobolev spaces in strictly pseudoconvex domains with minimal smoothness

Let $Ω\subset\mathbb{C}^n$ be a strictly pseudoconvex Runge domain with $C^2$-smooth defining function, $l\in\mathbb{N},$ $p\in(1,\infty).$ We prove that the holomorphic function $f$ has derivatives of order $l$ in $H^p(Ω)$ if and only if there exists a sequence on polynomials $P_n$ of degree $n$ such that $\sum\limits_{k=1}^{\infty}2^{2lk}\left\lvert f(z)-P_{2^k}(z) \right\rvert^2\in L^p(\partialΩ).$

math.CV↗

arXiv2019

Constructive description of analytic Besov spaces in strictly pseudoconvex domains

We use the method of pseudoanalytic continuation to obtain a characterization of spaces of holomorphic functions with boundary values in Besov spaces in terms of polynomial approximations.

math.CV↗

arXiv2017

External area integral inequality for the Cauchy-Leray-Fantappié integral

In this paper we extend Luzin inequality for functions deined by the Cauchy-Leray-Fantappié integral on the complement of a convex domain in $\mathbb{C}^n$. The work is supported by Russian Science Foundation Grant 14-41-00010.

math.CV↗