We show that ``Toeplitz like'' operators of the form T s u f=P s (uf ), where P s is a weighted Bergman projection, are bounded on the Hardy spaces H p , for 1 p< for certain ``symbols'' u defined on the unit disk. In particular, T s u is bounded if u is of the form u=h+G+ where h is a bounded harmo
Besov spaces and Bergman projections on the ball
✍ Scribed by H.Turgay Kaptanoğlu
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 62 KB
- Volume
- 335
- Category
- Article
- ISSN
- 1631-073X
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In this note we compute the weighted Bergman kernel of the unit ball with respect to the smallest norm in C n that extends the euclidian norm in R n . We establish the regularity properties of the corresponding weighted Bergman projection and give some applications.
One form of the celebrated theorem of Beurling states that if M is a z-invariant subspace of the Hardy space H 2 and P M is the orthogonal projection from H 2 onto M, then g = P M ( 1) is either a generator of M (that is M = gC[z]) or g = 0. In the latter case there is an n such that P M (z n ) gene