Geodesic
Norms of Complex Harmonic Projection Operators
Canadian journal of mathematics, Tome 55 (2003) no. 6, pp. 1134-1154

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we estimate the $\left( {{L}^{p}}-{{L}^{2}} \right)$ -norm of the complex harmonic projectors $\pi \ell {\ell }',\,1\le p\le 2$ , uniformly with respect to the indexes $\ell,{\ell}'$ . We provide sharp estimates both for the projectors ${{\pi }_{\ell{\ell}'}}$ , when $\ell,{\ell}'$ belong to a proper angular sector in $\mathbb{N}\,\times \,\mathbb{N}$ , and for the projectors ${{\pi }_{\ell0}}$ and ${{\pi }_{0\ell}}$ . The proof is based on an extension of a complex interpolation argument by C. Sogge. In the appendix, we prove in a direct way the uniform boundedness of a particular zonal kernel in the ${{L}^{1}}$ norm on the unit sphere of ${{\mathbb{R}}^{2n}}$ .
DOI : 10.4153/CJM-2003-045-6
Mots-clés : 43A85, 33C55, 42B15 
Casarino, Valentina. Norms of Complex Harmonic Projection Operators. Canadian journal of mathematics, Tome 55 (2003) no. 6, pp. 1134-1154. doi: 10.4153/CJM-2003-045-6
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