Optimal estimates for the gradient of harmonic functions in the unit disk

David Kalaj; Marijan Markovic

Optimal estimates for the gradient of harmonic functions in the unit disk

Complex Variables 2011-04-06 v2

Authors: David Kalaj , Marijan Markovic

Abstract

Concrete sharp constants in a pointwise estimate of the gradient of a harmonic function in the unit disk are obtained under the assumption that function belong to Hardy space $h^p$ , $p\ge 1$ . This generalizes some recent result of Maz'ya & Kresin and a result of Colonna related to the Bloch constant of harmonic mappings of the unit disk into itself.

Keywords

harmonic functions hardy spaces univalent functions

Cite

@article{arxiv.1012.3153,
  title  = {Optimal estimates for the gradient of harmonic functions in the unit disk},
  author = {David Kalaj and Marijan Markovic},
  journal= {arXiv preprint arXiv:1012.3153},
  year   = {2011}
}

Comments

14 pages, 2 figures

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