Extremal problems for vanishing functions in Bergman spaces
Adri\'an Llinares, Dragan Vukoti\'c
TL;DR
This paper establishes precise bounds for functions in weighted Bergman spaces that vanish at a point with a certain multiplicity, advancing understanding of extremal problems in complex analysis.
Contribution
It provides two sharp estimates for subspaces of weighted Bergman spaces with prescribed vanishing conditions, a novel contribution to extremal function theory.
Findings
Derived sharp bounds for vanishing functions in Bergman spaces
Enhanced understanding of extremal problems in weighted spaces
Contributed new estimates for functions with prescribed zeros
Abstract
We prove two sharp estimates for the subspace of a standard weighted Bergman space that consists of functions vanishing at a given point (with prescribed multiplicity).
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Harmonic Analysis Research · Algebraic and Geometric Analysis