Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T01:42:09.806Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Inequalities arising from a Banach algebra norm

Part of: Real functions Commutative Banach algebras and commutative topological algebras

Published online by Cambridge University Press:  09 April 2009

A. M. Russell
A. M. Russell
Affiliation:
Department of Mathematics University of Melbourne Parkville, Victoria 3052, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We derive some specific inequalities involving absolutely continuous functions and relate them to a norm inequality arising from Banach algebras of functions having bounded k th variation.

Keywords

absolutely continuous functiongeneralized bounded variationBanach algebra.

MSC classification

Secondary: 26A45: Functions of bounded variation, generalizations 46J10: Banach algebras of continuous functions, function algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 2 , April 1983 , pp. 199 - 202
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Berberian, S. K., ‘The character space of the algebra of regulated functions’, Pacific J. Math. 74 (1978), 15–36.CrossRefGoogle Scholar
[2]Dickmeis, G. and Dickmeis, W., Beste Approximation in Räumen von beschränkter p-Variation. Forschungerichte Des Landes Bordrhein-Westfalen Nr. 2697 Fachgruppe Mathematik/Informatik (Westdeuscher Verlag, 1977).CrossRefGoogle Scholar
[3]Hewitt, E. and Stromberg, K., Real and abstract analysis (Springer-Verlag, Berlin, Heidelberg, New York, 1969).Google Scholar
[4]Russell, A. M., ‘Functions of bounded k th variation’, Proc. London Math. Soc. (3) 26 (1973), 547–563.CrossRefGoogle Scholar
[5]Russell, A. M., ‘Further results on an integral representation of functions of generalized variation’, Bull. Austral. Math. Soc. 3 (1978), 407–420.CrossRefGoogle Scholar
[6]Russell, A. M., ‘A commutative Banach algebra of functions of generalized variation’, Pacific J. Math. 84 (1979), 455–463.CrossRefGoogle Scholar
[7]Russell, A. M., ‘A commutative Banach algebra of functions of bounded variation’, Amer. Math. Monthly 87 (1980), 39–40.CrossRefGoogle Scholar
[8]Upton, C. J. F., ‘An integral inequality associated with generalized variation’, Applicable Analysis, to appear.Google Scholar