K-functionals of fractional orders and moduli of smoothness on a general setting
Moduli of smoothness and K-functionals on the unit sphere and ball
| Full text | |
| Author(s): |
Carrijo, A. O.
;
Jordao, T.
;
Santos, C.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | POSITIVITY; v. 26, n. 3, p. 16-pg., 2022-07-01. |
| Abstract | |
We show an asymptotic relation between the fractional Peetre type K-functional and the modulus of smoothness on a compact two-point homogeneous space. This extends both: the well known results on the spherical setting and results for the modulus of smoothness with positive integer degree of smoothness. This is a natural continuation of the research including a previous characterization, obtained by first author in 2019 (Carrijo in Positivity 24:761-777, 2020). An application of the asymptotic relation obtained is employed to prove a reciprocal result for the standard decrease property of the degree of the fractional modulus of smoothness. (AU) | |
| FAPESP's process: | 19/02202-6 - Embeddings of functions spaces of generalized smoothness |
| Grantee: | Thaís Jordão |
| Support Opportunities: | Regular Research Grants |