Sharp Békollé estimates for the Bergman projection

Abstract

We prove sharp estimates for the Bergman projection in weighted Bergman spaces in terms of the Békollé constant. Our main tools are a dyadic model dominating the operator and an adaptation of a method of Cruz-Uribe, Martell and Pérez.2010 Mathematics Subject Classification. Primary: 47B38, 30H20 Secondary: 42C40, 42A61,42A50 .

Bergman projection induced by kernel with integral representation

“…is an orthogonal projection from L 2 ω to A 2 ω and it is closely related to the maximal Bergman projection The boundedness of projections on L p -spaces is an intriguing topic which presents obvious mathematical difficulties and has plenty of applications in operator theory [1,3,4,6,7,12,15,23,24]. It is known that for 1 < p < ∞ and d(ω ⊗ m) = dA α ,…”

Weighted Boundedness of Maximal Functions and Fractional Bergman Operators

“…is finite. This is the exact range of weights ω for which the orthogonal projection P α from L 2 (H, dV α (z)) onto its closed subspace consisting of analytic functions is bounded on L p (H, ωdV α ) (see [1,2,10]). For p = ∞, we say ω ∈ B ∞,α , if…”

Sharp Weighted Bounds for Multilinear Fractional Type Operators Associated with Bergman Projection

“…Lemma 8 (see [4]). Given an interval ⊂ R, there is a dyadic interval ∈ D , for some ∈ {0, 1/3}, such that ⊂ and | | ≤ 8| |.…”

“…Later on, for 1 < < ∞, Pott and Reguera [4] demonstrated the sharp Békollé estimates for the maximal Bergman projection as follows:…”