New Estimates for the Minimal L2 Solution of ∂̄ and Applications to Geometric Function Theory in Weighted Bergman Spaces
نویسنده
چکیده
The goal of this paper is to study two problems of geometric function theory in weighted Bergman spaces in the unit ball B in Cn. We treat both problems by making use of a theorem, which we prove, that gives improved estimates for the solution of minimal L2 norm for the ∂̄ equation. The technique we use to establish these improved estimates is a new method which we call double twisting. The double twisting technique is broad in scope, and should have many more applications, which we hope to demonstrate in future work. The particular kind of geometry we are interested in primarily concerns C 2-smooth weights φ whose curvature forms ddcφ satisfy
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