Loading...
Please wait, while we are loading the content...
Similar Documents
The Bergman spaces, the Bloch space, and Gleason’s problem
| Content Provider | Semantic Scholar |
|---|---|
| Author | Zhu, Kehe |
| Copyright Year | 1988 |
| Abstract | Suppose / is a holomorphic function on the open unit ball Bn of Cn. For 1 < p < oo and to > 0 an integer, we show that / is in Lp(Bn,dV) (with dV the volume measure) iff all the functions dmf/dza (\a\ = to) are in Lp(Bn,dV). We also prove that / is in the Bloch space of Bn iff all the functions dmf/dza (\a\ = m) are bounded on Bn. The corresponding result for the little Bloch space of Bn is established as well. We will solve Gleason's problem for the Bergman spaces and the Bloch space of Bn before proving the results stated above. The approach here is functional analytic. We make extensive use of the reproducing kernels of B„. The corresponding results for the polydisc in Cn are indicated without detailed proof. |
| Starting Page | 253 |
| Ending Page | 268 |
| Page Count | 16 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9947-1988-0931533-6 |
| Alternate Webpage(s) | http://www.ams.org/journals/tran/1988-309-01/S0002-9947-1988-0931533-6/S0002-9947-1988-0931533-6.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9947-1988-0931533-6 |
| Volume Number | 309 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
