On the higher-dimensional harmonic analog of the Levinson log log theorem

2014/07/18 by Alexander Logunov, Logunov, Alexander · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #math.AP #math.CA #math.CV

paper · pdf · doi:10.48550/arxiv.1407.4934

openalex publication_date 2014/07/18 · arxiv created 2014/08/05 · arxiv updated 2014/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M\colon (0,1) → [e,+∞) be a decreasing function such that ∫₀¹loglog M(y)dy<+∞. Consider the set H_M of all functions u harmonic in P:=\(x,y)∈ ℝⁿ: x∈ ℝ^n-1, y∈ ℝ, |x|<1, |y|<1 \ and satisfying |u(x,y)| ≤ M(|y|). We prove that H_M is a normal family in P.

Cited by

• Self-improving estimates of growth of subharmonic and analytic functions

Related

• An extension of Berwald's inequality and its relation to Zhang's\n inequality
• On an integral of J-Bessel functions and its application to Mahler measure (with an appendix by J.S. Friedman*)
• The integrals in Gradshteyn and Ryzhik. Part 1: An Addendum
• The integrals in Gradshteyn and Ryzhik. Part 1: An Addendum
• On the Liouville function in short intervals