On a conjecture about contractive inequalities for weighted Bergman spaces

2021/12/18 by Adrián Llinares, Llinares, Adrián
Mathematics · #30H10 #30H20 #47A30 #47B91 #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2112.09962

openalex publication_date 2021/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are interested in the norm of the inclusion between the standard weighted Bergman spaces A²_α and A^p_{(p)/(2) (α+ 2)-2}, p > 2, which is conjectured to be contractive by O.F. Brevig, J. Ortega-Cerdà, K. Seip and J. Zhao (in the limit case α= -1) and E. Lieb and J.P. Solovej (for α> -1). We provide some partial answers and improvements of some recent results.

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