Comptes Rendus
An inner function which is not weak outer
[Une fonction intérieure qui n'est pas faiblement extérieure]
Comptes Rendus. Mathématique, Volume 334 (2002) no. 11, pp. 957-960.

On construit une fonction intérieure I dans la boule unité B n telle que I(z)≠0 pour zB et le sous-espace IHp(B) n'est pas faiblement dense dans la classe de Hardy Hp(B), pour 0<p<1.

We construct a nonvanishing inner function I in the unit ball B n such that the subspace IHp(B) is not weakly dense in the Hardy space Hp(B), with 0<p<1.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02374-9

Evgueni Doubtsov 1

1 Department of Mathematics and Mechanics, St. Petersburg State University, Bibliotechnaya pl. 2, St. Petersburg 198904, Russia
@article{CRMATH_2002__334_11_957_0,
     author = {Evgueni Doubtsov},
     title = {An inner function which is not weak outer},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {957--960},
     publisher = {Elsevier},
     volume = {334},
     number = {11},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02374-9},
     language = {en},
}
TY  - JOUR
AU  - Evgueni Doubtsov
TI  - An inner function which is not weak outer
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 957
EP  - 960
VL  - 334
IS  - 11
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)02374-9
LA  - en
ID  - CRMATH_2002__334_11_957_0
ER  - 
%0 Journal Article
%A Evgueni Doubtsov
%T An inner function which is not weak outer
%J Comptes Rendus. Mathématique
%D 2002
%P 957-960
%V 334
%N 11
%I Elsevier
%R 10.1016/S1631-073X(02)02374-9
%G en
%F CRMATH_2002__334_11_957_0
Evgueni Doubtsov. An inner function which is not weak outer. Comptes Rendus. Mathématique, Volume 334 (2002) no. 11, pp. 957-960. doi : 10.1016/S1631-073X(02)02374-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02374-9/

[1] A.B. Aleksandrov The existence of inner functions in the ball, Mat. Sb., Volume 118(160) (1982) no. 2(6), pp. 147-163 (in Russian); English translation: Math. USSR-Sb. 46 (1983) 143–159

[2] A.B. Aleksandrov Function theory in the ball (G.M. Khenkin; A.G. Vitushkin, eds.), Several Complex Variables II, Encyclopaedia Math. Sci., 8, Springer, 1994, pp. 107-178

[3] P.L. Duren; B.W. Romberg; A.L. Shields Linear functionals on Hp spaces with 0<p<1, J. Reine Angew. Math., Volume 238 (1969), pp. 32-60

[4] J.W. Roberts Cyclic inner functions in the Bergman spaces and weak outer functions in Hp (0<p<1), Illinois J. Math., Volume 29 (1985), pp. 25-38

[5] W. Rudin New Constructions of Functions Holomorphic in the Unit Ball of n , CBMS Regional Conf. Ser. in Math., 63, American Mathematical Society, Providence, 1986

[6] H.S. Shapiro Some remarks on weighted polynomial approximation of holomorphic functions, Mat. Sb., Volume 73(115) (1967) no. 3, pp. 320-330 (in Russian)

[7] J.H. Shapiro Remarks on F-spaces of analytic functions, Lecture Notes in Math., 604, Springer-Verlag, 1977, pp. 107-124

[8] K. Zhu Operator Theory in Function Spaces, Marcel Dekker, New York, 1990

Cité par Sources :

Commentaires - Politique