Affine synthesis and coefficient norms for Lebesgue, Hardy and Sobolev spaces
| dc.creator | Bui, Huy-Qui | |
| dc.creator | Laugesen, Richard S. | |
| dc.date | 2006-08-29 | |
| dc.date | 2006-11-02 | |
| dc.date.accessioned | 2026-07-07T07:22:18Z | |
| dc.date.available | 2026-07-07T07:22:18Z | |
| dc.description | The affine synthesis operator is shown to map the mixed-norm sequence space $\ell^1(\ell^p)$ surjectively onto $L^p(\Rd), 1 \leq p < \infty$, assuming the Fourier transform of the synthesizer does not vanish at the origin and the synthesizer has some decay near infinity. Hence the standard norm on $f \in L^p(\Rd)$ is equivalent to the minimal coefficient norm of realizations of $f$ in terms of the affine system. We further show the synthesis operator maps a discrete Hardy space onto $H^1(\Rd)$, which yields a norm equivalence for Hardy space involving convolution with a discrete Riesz kernel sequence. Coefficient norm equivalences are established also for Sobolev spaces, by applying difference operators to the coefficient sequences. | |
| dc.description | Added references, and improved several proofs. Also added Appendix C, which connects the paper to Banach frame theory | |
| dc.identifier | https://arxiv.org/abs/math/0608738 | |
| dc.identifier | http://arxiv.org/abs/math/0608738 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115614 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 41A30; 42B30; 46E35 | |
| dc.title | Affine synthesis and coefficient norms for Lebesgue, Hardy and Sobolev spaces | |
| dc.type | text |