We give elementary proofs of the Forelli᎐Rudin estimates and generalizations of these estimates. As an application we obtain L p -boundedness results for classes of integral operators that include Bergman projections and Hankel operators.
Sharp Forelli–Rudin estimates and the norm of the Bergman projection
✍ Scribed by Liu, Congwen
- Book ID
- 126767031
- Publisher
- Elsevier Science
- Year
- 2015
- Tongue
- English
- Weight
- 948 KB
- Volume
- 268
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We give a new proof of the following inequality. In any dimension n G 2 and for Ž . 1-p-nlet s s n q p r2 p. Then p, s Ž n . where L R denotes the usual Sobolev space and ٌ¨denotes the gradient of The choice of s is optimal, as is the requirement that n ) p. In addition, some Sobolev norms of u ٌ¨
## Abstract We consider the Bergman projection on Henkin–Leiterer domains, bounded strictly pseudoconvex domains which have defining functions whose gradient is allowed to vanish. Our result describes the mapping properties of the Bergman projection between weighted __L^p^__ spaces, with the weight