The Composition Operator and the Space of the Functions of Bounded Variation in Schramm-Korenblum's Sense
We show that the composition operator H, associated with h:[a,b]→ℝ, maps the spaces Lip[a,b] on to the space κBVϕa,b of functions of bounded variation in Schramm-Korenblum's sense if and only if h is locally Lipschitz. Also, verify that if the composition operator generated by h:[a,b]×ℝ→ℝ maps...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/284389 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We show that the composition operator H, associated with h:[a,b]→ℝ, maps the spaces Lip[a,b] on to the space κBVϕa,b of functions of bounded variation in Schramm-Korenblum's sense if and only if h is locally Lipschitz. Also, verify that if the composition operator generated by h:[a,b]×ℝ→ℝ maps this space into itself and is uniformly bounded, then regularization of h is affine in the second variable. |
|---|---|
| ISSN: | 0972-6802 1758-4965 |