Functionals with extrema at reproducing kernels

• Published in: Geometric and functional analysis Vol. 32; no. 4; pp. 938 - 949
• Main Author: Kulikov, Aleksei
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.08.2022; Springer Nature B.V
• Subjects: Analysis; Kernels; Mathematics; Mathematics and Statistics

We show that certain monotone functionals on the Hardy spaces and convex functionals on the Bergman spaces are maximized at the normalized reproducing kernels among the functions of norm 1, thus proving the contractivity conjecture of Pavlović and of Brevig, Ortega-Cerdà, Seip and Zhao and the Wehrl...