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On Functions of Bounded (p,k)-Variation
Joint Authors
Sanchez, Jose Luis
Rivas, S.
Merentes, Nelson
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-02-08
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We introduce and study the concept of (p,k)-variation (1
In particular, we prove that a function u:[a,b]→ℝ has bounded (p,k)-variation if and only if u(k-1) is absolutely continuous on [a,b] and u(k) belongs to Lp[a,b].
Moreover, an explicit connection between the (p,k)-variation of u and the Lp-norm of u(k) is given which is parallel to the classical Riesz formula characterizing functions in the spaces RVp[a,b] and Ap[a,b].
This may also be considered as an alternative characterization of the one variable Sobolev space Wpk[a,b].
American Psychological Association (APA)
Merentes, Nelson& Rivas, S.& Sanchez, Jose Luis. 2012. On Functions of Bounded (p,k)-Variation. Journal of Function Spaces،Vol. 2012, no. 2012, pp.1-9.
https://search.emarefa.net/detail/BIM-994295
Modern Language Association (MLA)
Merentes, Nelson…[et al.]. On Functions of Bounded (p,k)-Variation. Journal of Function Spaces No. 2012 (2012), pp.1-9.
https://search.emarefa.net/detail/BIM-994295
American Medical Association (AMA)
Merentes, Nelson& Rivas, S.& Sanchez, Jose Luis. On Functions of Bounded (p,k)-Variation. Journal of Function Spaces. 2012. Vol. 2012, no. 2012, pp.1-9.
https://search.emarefa.net/detail/BIM-994295
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-994295