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 Mat. Sb., 2016, Volume 207, Number 1, Pages 151–166 (Mi msb8455)

On the density of certain modules of polyanalytic type in spaces of integrable functions on the boundaries of simply connected domains

K. Yu. Fedorovskiyab

a Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
b Bauman Moscow State Technical University

Abstract: We consider the question of the density in the space $L^p$, $1\leq p\leq\infty$, on the unit circle, of the subspaces $H^p+\sum_{k=1}^mw_kH^p$, where $H^p$ is the standard Hardy space and $w_1,…,w_m$ are given functions in the class $L^\infty$. This question is closely related to problems of uniform and $L^p$-approximations of functions by polyanalytic polynomials on the boundaries of simple connected domains in $\mathbb C$. The obtained results are formulated in terms of Nevanlinna and $d$-Nevanlinna domains, that is, in terms of special analytic characteristics of simply connected domains in $\mathbb C$, which are related to the pseudocontinuation property of bounded holomorphic functions.
Bibliography: 19 titles.

Keywords: Nevanlinna domain, $d$-Nevanlinna domain, pseudocontinuation, polyanalytic polynomial, uniform approximation, $L^p$-approximation.

 Funding Agency Grant Number Russian Science Foundation 14-21-00025 This research was supported by the Russian Science Foundation (project no. 14-21-00025).

DOI: https://doi.org/10.4213/sm8455

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English version:
Sbornik: Mathematics, 2016, 207:1, 140–154

Bibliographic databases:

UDC: 517.53
MSC: Primary 30E10, 30G20; Secondary 41A10

Citation: K. Yu. Fedorovskiy, “On the density of certain modules of polyanalytic type in spaces of integrable functions on the boundaries of simply connected domains”, Mat. Sb., 207:1 (2016), 151–166; Sb. Math., 207:1 (2016), 140–154

Citation in format AMSBIB
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