Properties of Functions in the Wiener ClassBVp[a,b]for0 Published:2015 Issue: Volume:2015 Page:1-4 ISSN:2314-8896 Container-title:Journal of Function Spaces language:en Short-container-title:Journal of Function Spaces Author: Niu Yeli1,Wang Heping2ORCID Affiliation: 1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China2. School of Mathematical Sciences, BCMIIS, Capital Normal University, Beijing 100048, China Abstract We will investigate properties of functions in the Wiener classBVp[a,b]with0<p<1. We prove that any function inBVp[a,b] (0<p<1)can be expressed as the difference of two increasing functions inBVp[a,b]. We also obtain the explicit form of functions inBVp[a,b]and show that their derivatives are equal to zero a.e. on[a,b]. Funder National Natural Science Foundation of China Publisher Hindawi Limited Subject Analysis Link http://downloads.hindawi.com/journals/jfs/2015/630137.pdf Reference10 articles. 1. On convergence of Fourier series of functions of generalized bounded variation2. Some Generalizations of the Notion of Bounded Variation3. Absolute convergence of Fourier series of functions of λBV(p) and ϕλBV4. Generalized absolute continuity of a function of Wiener's class
Author:
Affiliation:
1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
2. School of Mathematical Sciences, BCMIIS, Capital Normal University, Beijing 100048, China
Abstract
Funder
National Natural Science Foundation of China
Publisher
Hindawi Limited
Subject
Analysis
Link
http://downloads.hindawi.com/journals/jfs/2015/630137.pdf
Reference10 articles.
1. On convergence of Fourier series of functions of generalized bounded variation
2. Some Generalizations of the Notion of Bounded Variation
3. Absolute convergence of Fourier series of functions of λBV(p) and ϕλBV
4. Generalized absolute continuity of a function of Wiener's class
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