Norms of Complex Harmonic Projection Operators

[摘要] In this paper we estimate the $(L^p-L^2)$-norm of the complexharmonic projectors $pi_{ellell'}$, $1le ple 2$, uniformlywith respect to the indexes $ell,ell'$. We provide sharpestimates both for the projectors $pi_{ellell'}$, when$ell,ell'$ belong to a proper angular sector in $mathbb{N}imes mathbb{N}$, and for the projectors $pi_{ell 0}$ and$pi_{0 ell}$. The proof is based on an extension of a complexinterpolation argument by C.~Sogge. In the appendix, we prove in adirect way the uniform boundedness of a particular zonal kernel inthe $L^1$ norm on the unit sphere of $mathbb{R}^{2n}$.

[学科分类] 数学（综合）