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

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

2010-12-14

arxiv.org/abs/1012.3153v2

Mathematics

Complex Variables

14 pages, 2 figures

Scientific paper

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.

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