On the Vector valued Fourier Transform And Compatibility of Operators
| dc.creator | Park, In Sook | |
| dc.date | 2002-08-30 | |
| dc.date | 2003-10-20 | |
| dc.date.accessioned | 2026-07-07T12:32:40Z | |
| dc.date.available | 2026-07-07T12:32:40Z | |
| dc.description | Let $\mathbb{G}$ be a locally compact abelian group and let $1<p\leq 2$. $\mathbb{G}^{'}$ is the dual group of $\mathbb{G}$, and $p^{'}$ the conjugate exponent of $p$. An operator $T$ between Banach spaces $X$ and $Y$ is said to be compatible with the Fourier transform $F^{\mathbb{G}}$ if $F^{\mathbb{G}}\otimes T: L_p(\mathbb{G})\otimes X\to L_{p^{'}}(\mathbb{G}^{'})\otimes Y $ admits a continuous extension $[F^{\mathbb{G}},T]:[L_p(\mathbb{G}),X]\to [L_{p^{'}}(\mathbb{G}^{'}),Y]$. $\mathcal{FT}_p^{\mathbb{G}}$ denotes the set of such $T$'s. We show that $\mathcal{FT}_p^{\mathbb{R}\times\mathbb{G}}=\mathcal{FT}_p^{\mathbb{Z}\times\m athbb{G}} =\mathcal{FT}_p^{\mathbb{Z}^n \times\mathbb{G}}$ for any $\mathbb{G}$ and positive integer $n$. And if the factor group of $\mathbb{G}$ with respect to its component of the identity element is a direct sum of a torsion free group and a finite group with discrete topology then $\mathcal{FT}_p^{\mathbb{G}}=\mathcal{FT}_p^{\mathbb{Z}}$ . | |
| dc.description | Submitted at June, 2002. Changes in this revision: i) I correct a mistake in the proof of Lemma 13, but the statement is not changed. (ii) I rewrite the abstract more simple and clearly understood. But the meaning is not changed | |
| dc.identifier | https://arxiv.org/abs/math/0208253 | |
| dc.identifier | http://arxiv.org/abs/math/0208253 | |
| dc.identifier | Studia Math. 168 (2), pp 95-108, 2005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216855 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 46B20; 46B07 | |
| dc.title | On the Vector valued Fourier Transform And Compatibility of Operators | |
| dc.type | text |