Strong convergence of approximate identities and Bourgain points of bounded functions
type: Item
instance of: scholarly article
title: Strong convergence of approximate identities and Bourgain points of bounded functions
zbMATH Open document ID: 1184.42003
DOI: 10.1134/S1064562408050360
published in: Doklady Mathematics
publication date: 2010-01-12T00:00:00Z
review text: The author first describes a class \(\Phi\) such that any bounded function is strongly (in the sense of Lim) approximated by the convolutions \(u^f_\Phi(x,y)\) at each of its \(B\)-points \(x\). Next, he describes the kernels \(\Phi\) such that \(\text{Lim}_{y\to -} u^f_\Phi(x,y)\) for a real-valued \(f\in C(\mathbb{R})\cap L^\infty(\mathbb{R})\) does not exist at all points \(x\in\mathbb{R}\). The paper also contains a geometrical description of \(B\)-pints of Cantor-type perfect sets. A multidimensional analogue of a result obtained in this paper is also mentioned.
reviewed by: Som Prakash Goyal
Mathematics Subject Classification ID: 42A38
Mathematics Subject Classification ID: 26A45
zbMATH DE Number: 5656100
zbMATH Keywords: strong convergence
zbMATH Keywords: Bourgain points
zbMATH Keywords: bounded functions
zbMATH Keywords: Cantor-type perfect set
author: Pavel Mozolyako
MaRDI profile type: Publication
cites work: On the radial variation of bounded analytic functions on the disc
cites work: The radial variation of analytic functions
cites work: Q5848315
cites work: Vertical variation of harmonic functions in upper half-spaces
cites work: A Complete Bounded Complex Submanifold of C 3
full work available at URL: s1064562408050360
OpenAlex ID: W1963590872
description: scientific article; zbMATH DE number 5656100