Geodesic
Lipschitz Type Characterizations for Bergman Spaces
Canadian mathematical bulletin, Tome 52 (2009) no. 4, pp. 613-626

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

We obtain new characterizations for Bergman spaces with standard weights in terms of Lipschitz type conditions in the Euclidean, hyperbolic, and pseudo-hyperbolic metrics. As a consequence, we prove optimal embedding theorems when an analytic function on the unit disk is symmetrically lifted to the bidisk.
DOI : 10.4153/CMB-2009-060-6
Mots-clés : 32A36, Bergman spaces, hyperbolic metric, Lipschitz condition 
Wulan, Hasi; Zhu, Kehe. Lipschitz Type Characterizations for Bergman Spaces. Canadian mathematical bulletin, Tome 52 (2009) no. 4, pp. 613-626. doi: 10.4153/CMB-2009-060-6
@article{10_4153_CMB_2009_060_6,
     author = {Wulan, Hasi and Zhu, Kehe},
     title = {Lipschitz {Type} {Characterizations} for {Bergman} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {613--626},
     year = {2009},
     volume = {52},
     number = {4},
     doi = {10.4153/CMB-2009-060-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-060-6/}
}
TY  - JOUR
AU  - Wulan, Hasi
AU  - Zhu, Kehe
TI  - Lipschitz Type Characterizations for Bergman Spaces
JO  - Canadian mathematical bulletin
PY  - 2009
SP  - 613
EP  - 626
VL  - 52
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-060-6/
DO  - 10.4153/CMB-2009-060-6
ID  - 10_4153_CMB_2009_060_6
ER  - 
%0 Journal Article
%A Wulan, Hasi
%A Zhu, Kehe
%T Lipschitz Type Characterizations for Bergman Spaces
%J Canadian mathematical bulletin
%D 2009
%P 613-626
%V 52
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-060-6/
%R 10.4153/CMB-2009-060-6
%F 10_4153_CMB_2009_060_6

[1] [1] Duren, P. and Schuster, A., Bergman spaces. Mathematical Surveys and Monographs 100, American Mathematical Society, Providence, RI, 2004. Google Scholar

[2] [2] Duren, P. and Shields, A., Restriction of Hp functions to the diagonal of the polydisk. Duke Math. J. 42(1975), no. 4, 751–753. Google Scholar

[3] [3] Garnett, J., Bounded analytic functions. Pure and Applied Mathematics 96, Academic Press, New York, 1981. Google Scholar

[4] [4] Hajlasz, P., Sobolev spaces on an arbitrary metric space. Potential Anal. 5(1996), no. 4, 403–415. Google Scholar

[5] [5] Hajlasz, P., Sobolev spaces on metric-measure spaces. In: Heat kernels and analysis on manifolds, graphs, and metric spaces, Contemp. Math. 338, American Mathematical Society, Providence, RI, 2003, pp. 173–218. Google Scholar

[6] [6] Hedenmalm, H., Korenblum, B., and Zhu, K., Theory of Bergman spaces. Graduate Texts in Mathematics 199, Springer-Verlag, New York, 2000. Google Scholar

[7] [7] Hedenmalm, H. and Shimorin, S., Weighted Bergman spaces and the integral means spectrum of conformal mappings. Duke Math. J. 127(2005), no. 2, 341–393. Google Scholar

[8] [8] Hedenmalm, H., Shimorin, S., and Sola, A., Norm expansion along a zero variety. J. Funct. Anal. 254(2008), no. 6, 1601–1625. Google Scholar

[9] [9] Horowitz, C. and Oberlin, D. M., Restriction of Hp() functions to the diagonal of . Indiana Univ. Math. J. 24(1974/75), 767–772. Google Scholar

[10] [10] Koskela, P. and Saksman, E., Pointwise characterizations of Hardy-Sobolev functions. Math. Res. Lett. 15(2008), no. 4, 727–744. Google Scholar

[11] [11] Rudin, W., Function theory in the Unit Ball of ℂ n. Fundamental Principles in Mathematical Science 241, Springer-Verlag, New York-Berlin, 1980. Google Scholar

[12] [12] Shamoyan, F. A., Applications of Dzhrbashyan integral representations to some problems of analysis. Dokl. Akad. Nauk SSSR 261(1981), no. 3, 557–561. Google Scholar

[13] [13] Stessin, M. and Zhu, K., Composition operators on embedded disks. J. Operator Theory 56(2006), no. 2, 423–449. Google Scholar

[14] [14] Zhu, K., Spaces of holomorphic functions in the unit ball. Graduate Texts in Mathematics 226, Springer-Verlag, New York, 2005. Google Scholar

Cité par Sources :