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arXiv · 0910.5750

A quasi-commutativity property of the Poisson and composition operators

Alberto Cialdea·Vladimir Maz'ya
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Abstract

Let $Φ$ be a real valued function of one real variable, let $L$ denote an elliptic second order formally self-adjoint differential operator with bounded measurable coefficients, and let $P$ stand for the Poisson operator for $L$. A necessary and sufficient condition on $Φensuring the equivalence of the Dirichlet integrals of $Φ\circ Ph$ and $P(Φ\circ h)$ is obtained. We illustrate this result by some sharp inequalities for harmonic functions.

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Alberto Cialdea, Vladimir Maz'ya. 2009-10-29. A quasi-commutativity property of the Poisson and composition operators. https://arxiv.org/abs/0910.5750

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