Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.00652 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We study the concept of (generalized) $p$-th variation of a real-valued continuous function along a general class of refining sequence of partitions. We show that the finiteness of the $p$-th variation of a given function is closely related to the finiteness of $\ell^p$-norm of the coefficients along a Schauder basis, similar to the fact that Hölder coefficient of the function is connected to $\ell^{\infty}$-norm of the Schauder coefficients. This result provides an isomorphism between the space of $α$-Hölder continuous functions with finite (generalized) $p$-th variation along a given partition sequence and a subclass of infinite-dimensional matrices equipped with an appropriate norm, in the spirit of Ciesielski.