p-Lambda-bounded variation

Document Type: Research Paper

Authors

Abstract

A characteriation of continuity of the $p$-$Lambda$-variation function is given and
the Helly's selection principle for
$Lambda BV^{(p)}$ functions is established.
A characterization of the inclusion of Waterman-Shiba classes into
classes of functions with given integral modulus of continuity is given.
A useful estimate on modulus of variation of functions of class $Lambda BV^{(p)}$ is found.

Keywords

History

• Receive Date: 01 November 2009
• Revise Date: 04 April 2010
• Accept Date: 04 April 2010