Norms of Complex Harmonic Projection Operators

Abstract

AbstractIn this paper we estimate the (Lp – L2)-norm of the complex harmonic projectors πℓ,ℓ′, 1 ≤ p ≤ 2, uniformly with respect to the indexes ℓ, ℓ′. We provide sharp estimates both for the projectors πℓ,ℓ′, when ℓ, ℓ′ belong to a proper angular sector in ℕ × ℕ, and for the projectors πℓ0 and π0ℓ. 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 L1 norm on the unit sphere of ℝ2n.