On Functions of Bounded (p,k)‎-Variation

Joint Authors

Sanchez, Jose Luis
Rivas, S.
Merentes, Nelson

Source

Journal of Function Spaces

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

Mathematics

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