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

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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