Hardy spaces and partial derivatives of conjugate harmonic functions

Ryabogin, Anatoly; Ryabogin, Dmitry

doi:10.1090/S0002-9939-07-08940-X

Hardy spaces and partial derivatives of conjugate harmonic functions
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by Anatoly Ryabogin and Dmitry Ryabogin

Proc. Amer. Math. Soc. 135 (2007), 2461-2470

DOI: https://doi.org/10.1090/S0002-9939-07-08940-X

Published electronically: April 5, 2007

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Abstract:

In this paper we give necessary and sufficient conditions for a harmonic vector and all its partial derivatives to belong to $H^p(\mathbf {R}^{n+1}_+)$ for all $p>0$.

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