Abstract
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.
Original language | English (US) |
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Article number | 124040 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 487 |
Issue number | 2 |
DOIs | |
State | Published - Jul 15 2020 |
Keywords
- Dual norm
- Hardy space
- Harmonic mapping
- Matrix norm
- Polynomial
ASJC Scopus subject areas
- Analysis
- Applied Mathematics