Abstract
AbstractWe consider mixed-norm Bergman spaces on homogeneous Siegel domains. In the literature, two different approaches have been considered and several results seem difficult to be compared. In this paper, we compare the results available in the literature and complete the existing ones in one of the two settings. The results we present are as follows: natural inclusions, density, completeness, reproducing properties, sampling, atomic decomposition, duality, continuity of Bergman projectors, boundary values, and transference.
Funder
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Publisher
Springer Science and Business Media LLC
Subject
Numerical Analysis,Analysis,Mathematics (miscellaneous)
Reference38 articles.
1. Békollé, D.: Bergman spaces with small exponents. Indiana U. Math. J. 49, 973–993 (2000)
2. Békollé, D., Bonami, A., Garrigós, G., Ricci, F.: Littlewood–Paley decompositions related to symmetric cones and Bergman projections in tube domains. Proc. Lond. Math. Soc. 89, 317–360 (2004)
3. Békollé, D., Bonami, A., Garrigós, G., Nana, C., Peloso, M.M., Ricci, F.: Lecture notes on Bergman projectors in tube domains over cones: an analytic and geometric viewpoint. IMHOTEP J. Afr. Math. Pures Appl. 5, 1–75 (2004)
4. Békollé, D., Bonami, A., Garrigós, G., Ricci, F., Sehba, B.: Analytic Besov spaces and Hardy-type inequalities in tube domains over symmetric cones. J. Reine Angew. Math. 647, 25–56 (2010)
5. Békollé, D., Bonami, A., Peloso, M.M., Ricci, F.: Boundedness of Bergman projections on tube domains over light cones. Math. Z. 237, 31–59 (2001)