Geodesic
Projections on Bergman Spaces Over Plane Domains
Canadian journal of mathematics, Tome 31 (1979) no. 6, pp. 1269-1280

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

Let D be a bounded plane domain and let Lp(D) stand for the usual Lebesgue spaces of functions with domain D, relative to the area Lebesque measure dσ(z) = dxdy. The class of all holomorphic functions in D will be denoted by H(D) and we write Bp(D) = Lp(D) ∩ H(D). Bp(D) is called the Bergman p-space and its norm is given by Let be the Bergman kernel of D and consider the Bergman projection (1.1) It is well known that P is not bounded on Lp(D), p = 1, ∞, and moreover, it can be shown that there are no bounded projections of L∞ (Δ) onto B∞ (Δ). 
Burbea, Jacob. Projections on Bergman Spaces Over Plane Domains. Canadian journal of mathematics, Tome 31 (1979) no. 6, pp. 1269-1280. doi: 10.4153/CJM-1979-105-6
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