In this paper, we establish an injectivity theorem on a weakly pseudoconvex Kähler manifold X with negative sectional curvature. For this purpose, we develop the harmonic theory in this circumstance. The negative sectional curvature condition is usually satisfied by the manifolds with hyperbolicity, such as symmetric spaces, bounded symmetric domains in Cn, hyperconvex bounded domains, and so on.
AbstractWe determine the eigenvalues of certain “fundamental” K-invariant Toeplitz type operators on weighted Bergman spaces over bounded symmetric domains $$D=G/K,$$
D
=
G
/
K
,
for the irreducible K-types indexed by all partitions of length $$r={\mathrm {rank}}(D)$$
r
=
rank
(
D
)
.
$$\mathbb{K}$$-homogeneous tuple of operators on bounded symmetric domains
