Embeddings of the classes \(H^\omega\)
type: Item
instance of: scholarly article
title: Embeddings of the classes \(H^\omega\)
zbMATH Open document ID: 0959.46022
DOI: 10.1007/BF02316286
author: M. V. Medvedeva
published in: Mathematical Notes
publication date: 2001-05-01T00:00:00Z
review text: The author proves two theorems giving necessary and sufficient conditions for embedding relations. One of them states the following attractive result: For the embedding \(H^\omega\subset\Lambda BV\), it is necessary and sufficient that for any sequence \(\{t_k\}\) such that \(t_k\geq 0\) and \(\sum^\infty_{k=1} t_k\leq 1\) the series \(\sum^\infty_{k=1} \omega(t_k) \lambda^{-1}_k\) be convergent, where \(\lambda_k\nearrow \infty\) and \(\sum \lambda^{-1}_k= \infty\), moreover \(\Lambda BV\) denotes the functions satisfying the condition \[ \sup_G \sum^N_{k=1}|f(b_k)- f(a_k)|\lambda^{-1}_k< \infty, \] the supremum is taken over all systems \(G\) of nonintersecting intervals \((a_k,b_k)\) belonging to the closed interval \([a,b]\) where \(f\) is given.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 26A45
zbMATH DE Number: 1407580
zbMATH Keywords: embedding relations
reviewed by: László Leindler
MaRDI profile type: Publication
cites work: Q4722541
cites work: On convergence of Fourier series of functions of generalized bounded variation
full work available at URL: https://doi.org/10.1007/bf02316286
OpenAlex ID: W1481733404
description: scientific article; zbMATH DE number 1407580