We obtain optimal size estimates of the harmonic Bergman kernel and its derivatives on smooth domains. Based on these estimates we derive mapping properties of the harmonic Bergman projection on Lebesgue spaces and Lipschitz spaces.
Bibliographical noteFunding Information:
1The first author’s research was partially supported by KOSEF 98-0701-03-01-5 and a grant from SNU and the second author’s research was partially supported by KOSEF 981-0102-009-2. We thank the referee for pointing out the relevance of Lemma 3.1 in [FR] to Theorem 4.2 of this paper. We also thank Professor D. Sarason for helpful suggestions.
- Biharmonic equations
- Harmonic Bergman kernel
- Harmonic Bergman projection
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