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

Leonid V. Kovalev, Xuerui Yang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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 languageEnglish (US)
Article number124040
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - Jul 15 2020


  • Dual norm
  • Hardy space
  • Harmonic mapping
  • Matrix norm
  • Polynomial

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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