Weissler and Bernoulli type inequalities in Bergman spaces

2023/02/10 by Anton Baranov, Baranov, Anton D., I. R. Kayumov +5
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2302.05522

openalex publication_date 2023/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Weissler type inequalities for Bergman spaces with general radial weights and give conditions on the weight w in terms of its moments ensuring that ‖f_r‖_A²ⁿ(w)≤ ‖f‖_A²(w) whenever n∈ ℕ and 0< r≤ 1/√(n). For noninteger exponents a special case of this inequality is proved which can be considered as a certain analog of the Bernoulli inequality. An example of a monotonic weight is constructed for which these inequalities are no longer true.

Related

• Two weights inequality for Hankel operators on weighted Bergman spaces induced by radial weights
• Weighted norm inequalities for derivatives on Bergman spaces
• Two weight inequality for Bergman projection
• Da Lio-Rivière-Wettstein-type inequality for weighted Bergman spaces
• Bergman kernels for Paley-Wiener spaces and Nazarov's proof of the Bourgain-Milman theorem