Let {λ 2} and {φ{symbol} λ } be the eigenvalues and an orthonormal system of eigenvectors of a second order elliptic differential operator Δ on a compact manifold M of dimension N. We prove that the Riesz means of order δ, defined by {Mathematical expression}, are uniformly bounded from the Hardy space H p (M) into Weak-L p (M), if 0<p<1 and δ=N/p-(N+1)/2. © 1988 Birkhäuser-Verlag.
Colzani, L. (1988). Riesz means of eigenfunction expansions of elliptic differential operators on compact manifolds. RENDICONTI DEL SEMINARIO MATEMATICO E FISICO DI MILANO, 58, 149-167.
Riesz means of eigenfunction expansions of elliptic differential operators on compact manifolds
COLZANI, LEONARDO
1988
Abstract
Let {λ 2} and {φ{symbol} λ } be the eigenvalues and an orthonormal system of eigenvectors of a second order elliptic differential operator Δ on a compact manifold M of dimension N. We prove that the Riesz means of order δ, defined by {Mathematical expression}, are uniformly bounded from the Hardy space H p (M) into Weak-L p (M), if 0
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