Geodesic
The Bergman Projection on Weighted Norm Spaces
Canadian journal of mathematics, Tome 32 (1980) no. 4, pp. 979-986

Voir la notice de l'article provenant de la source Cambridge University Press

Quite recently Bekollé and Bonami [1] have characterized the weighted measures λ on the unit disk Δ for which the Bergman projection is bounded on Lp (Δ : λ), 1 < p < ∞. Our methods in [4] can be applied to even extend their result by replacing the unit disk with multiply connected domains. This is done via a rather interesting identity between the Bergman kernel and its “adjoint” [2]. As a corollary of our result we obtain a generalization of a result due to Shikhvatov [7].Let D be a bounded plane domain and let λ be a positive locally integrate function in D. λ is said to belong to Mp(D) (1 < p < ∞) if it satisfies the Muckenhoupt condition: where the supremum is taken over all sectors V ⊂ D, dσ is the area Lebesgue measure and |V| = σ(V). 
Burbea, Jacob. The Bergman Projection on Weighted Norm Spaces. Canadian journal of mathematics, Tome 32 (1980) no. 4, pp. 979-986. doi: 10.4153/CJM-1980-075-5
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[7] 7. Shikhvatov, A. M., Spaces of analytic functions in a region with an angle, Mat. Zametki 18 (1975), 411–420. Google Scholar

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