Closed Ideals in Some Algebras of Analytic Functions
Canadian journal of mathematics, Tome 61 (2009) no. 2, pp. 282-298

Voir la notice de l'article provenant de la source Cambridge University Press

We obtain a complete description of closed ideals of the algebra $\mathcal{D}\cap \text{li}{{\text{p}}_{\alpha }},0<\alpha \le \frac{1}{2}$ , where $\mathcal{D}$ is the Dirichlet space and $\text{li}{{\text{p}}_{\alpha }}$ is the algebra of analytic functions satisfying the Lipschitz condition of order $\alpha $ .
DOI : 10.4153/CJM-2009-014-5
Mots-clés : 46E20, 30H05, 47A15
Bouya, Brahim. Closed Ideals in Some Algebras of Analytic Functions. Canadian journal of mathematics, Tome 61 (2009) no. 2, pp. 282-298. doi: 10.4153/CJM-2009-014-5
@article{10_4153_CJM_2009_014_5,
     author = {Bouya, Brahim},
     title = {Closed {Ideals} in {Some} {Algebras} of {Analytic} {Functions}},
     journal = {Canadian journal of mathematics},
     pages = {282--298},
     year = {2009},
     volume = {61},
     number = {2},
     doi = {10.4153/CJM-2009-014-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2009-014-5/}
}
TY  - JOUR
AU  - Bouya, Brahim
TI  - Closed Ideals in Some Algebras of Analytic Functions
JO  - Canadian journal of mathematics
PY  - 2009
SP  - 282
EP  - 298
VL  - 61
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2009-014-5/
DO  - 10.4153/CJM-2009-014-5
ID  - 10_4153_CJM_2009_014_5
ER  - 
%0 Journal Article
%A Bouya, Brahim
%T Closed Ideals in Some Algebras of Analytic Functions
%J Canadian journal of mathematics
%D 2009
%P 282-298
%V 61
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2009-014-5/
%R 10.4153/CJM-2009-014-5
%F 10_4153_CJM_2009_014_5

[1] [1] Carleson, L., A representation formula for the Dirichlet space. Math. Z. 73(1960), 190–196. Google Scholar

[2] [2] El-Fallah, O., Kellay, K., and Ransford, T., Cyclicity in the Dirichlet space. Ark. Mat. 44(2006), no. 1, 61–86. Google Scholar

[3] [3] Esterle, J., Strouse, E., and Zouakia, F., Closed ideals of A + and the Cantor set. J. Reine Angew. Math. 449(1994), 65–79. Google Scholar

[4] [4] Hedenmalm, H. and Shields, A., Invariant subspaces in Banach spaces of analytic functions. Michigan Math. J. 37(1990), no. 1, 91–104. Google Scholar

[5] [5] Hoffman, K., Banach spaces of analytic functions. Reprint of the 1962 original, Dover Publications Inc., New York, 1988. Google Scholar

[6] [6] Korenbljuum, B. I., Invariant subspaces of the shift operator in a weighted Hilbert space. Mat. Sb. 89(131)(1972), 110–137, 166. Google Scholar

[7] [7] Matheson, A., Approximation of analytic functions satisfying a Lipschitz condition. Michigan Math. J. 25(1978), no. 3, 289–298. Google Scholar

[8] [8] Shamoyan, F. A., Closed ideals in algebras of functions that are analytic in the disk and smooth up to its boundary. Mat. Sb. 79(1994), no. 2, 425–445. Google Scholar

[9] [9] Shirokov, N. A., Analytic functions smooth up to the boundary. Lecture notes in mathematics 1312, Springer-Verlag, Berlin, 1988. Google Scholar

[10] [10] Shirokov, N. A., Closed ideals of algebras of type B α pq. Izv. Akad. Nauk. SSSR Ser. Mat. 46(1982), no. 6, 1316–1332, 1344. Google Scholar

[11] [11] Taylor, B. A. and Williams, D. L., Ideals in rings of analytic functions with smooth boundary values. Canad J. Math. 22(1970), 1266–1283. Google Scholar

Cité par Sources :