On the setting of general bounded smooth domains in Rn, we construct L1-bounded nonorthogonal projections and obtain related reproducing formulas for the harmonic Bergman spaces. In addition, we show that those projections satisfy Sobolev Lp -estimates of any order even for p=1. Among applications are Gleason's problems for the harmonic Bergman-Sobolev and (little) Bloch functions on star-shaped domains with strong reference points.
|Number of pages||34|
|Journal||Journal of Functional Analysis|
|Publication status||Published - 2004 Nov 15|
- Gleason's problem
- Harmonic Bergman function
ASJC Scopus subject areas