A new family of sharp conformally invariant integral inequalities

Details A new family of sharp conformally invariant integral inequalities A new family of sharp conformally invariant integral inequalities

2010-08-07

arxiv.org/abs/1008.1301v2

Mathematics

Functional Analysis

17 pages

Scientific paper

We prove a one-parameter family of sharp integral inequalities for functions on the $n$-dimensional unit ball. The inequalities are conformally invariant, and the sharp constants are attained for functions that are equivalent to a constant function under conformal transformations. As a limiting case, we obtain an inequality that generalizes Carleman's inequality for harmonic functions in the plane to poly-harmonic functions in higher dimensions.

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