Isomorphisms of Royden Type Algebras Over $\mathbb{S}^1$

Radice, Teresa; Saksman, Eero; Zecca, Gabriella

Isomorphisms of Royden Type Algebras Over

\mathbb{S}^{1}

Radice, Teresa ; Saksman, Eero ; Zecca, Gabriella

Bollettino dell'Unione Matematica Italiana, Tome 2 (2009), p. 719-729 / Harvested from Biblioteca Digitale Italiana di Matematica

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Résumé

Let $\mathbb{S}^{1}$ and $\mathbb{D}$ be the unit circle and the unit disc in the plane and let us denote by $\mathcal{A}(\mathbb{S}^{1})$ the algebra of the complex-valued continuous functions on $\mathbb{S}^{1}$ which are traces of functions in the Sobolev class $W^{1,2}(\mathbb{D})$ . On $\mathcal{A}(\mathbb{S}^{1})$ we define the following norm $\|u\|=\|u\|_{L^{\infty}(\mathbb{S}^{1})}+\left(\iint_{\mathbb{D}}|\nabla\tilde% {u}|^{2}\right)^{1/2}$ where is the harmonic extension of $u$ to $\mathbb{D}$ . We prove that every isomorphism of the functional algebra $\mathcal{A}(\mathbb{S}^{1})$ is a quasitsymmetric change of variables on $\mathbb{S}^{1}$ .

Publié le : 2009-10-01

MR 2569300 | Zbl 1191.30009

@article{BUMI_2009_9_2_3_719_0,
     author = {Teresa Radice and Eero Saksman and Gabriella Zecca},
     title = {Isomorphisms of Royden Type Algebras Over $\mathbb{S}^1$},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {2},
     year = {2009},
     pages = {719-729},
     zbl = {1191.30009},
     mrnumber = {2569300},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2009_9_2_3_719_0}
}

Radice, Teresa; Saksman, Eero; Zecca, Gabriella. Isomorphisms of Royden Type Algebras Over $\mathbb{S}^1$. Bollettino dell'Unione Matematica Italiana, Tome 2 (2009) pp. 719-729. http://gdmltest.u-ga.fr/item/BUMI_2009_9_2_3_719_0/

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