Near-isometric duality of Hardy norms with applications to harmonic mappings

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:487

Article

Kovalev, Leonid, V¹  Yang, Xuerui¹ 

[1] Syracuse Univ, Math Dept, 215 Carnegie, Syracuse, NY 13244 USA

关键词: Hardy space;    Polynomial;    Dual norm;    Harmonic mapping;    Matrix norm;   

DOI  :  10.1016/j.jmaa.2020.124040

来源: Elsevier

【 摘 要 】

Hardy spaces in the complex plane and in higher dimensions have natural finite-dimensional subspaces formed by polynomials or by linear maps. We use the restriction of Hardy norms to such subspaces to describe the set of possible derivatives of harmonic self-maps of a ball, providing a version of the Schwarz lemma for harmonic maps. These restricted Hardy norms display unexpected near-isometric duality between the exponents 1 and 4, which we use to give an explicit form of harmonic Schwarz lemma. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free