Pointwise multiplicative inequalities and Nirenberg type estimates in weighted Sobolev spaces
The aim of this paper is to give a description of the Poisson kernel and the Green function of balls in the complex hyperbolic space. The description is in terms of the hypergeometric function and unitary spherical harmonics in ℂⁿ.
In this paper, we give a sharp estimate on the dimension of the space of polynomial growth harmonic functions with fixed degree on a complete Riemannian manifold, under various assumptions.
On the harmonic Bergman space of the ball, we give characterizations for an arbitrary positive Toeplitz operator to be a Schatten class operator in terms of averaging functions and Berezin transforms.
We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space into another for in terms of certain Carleson and vanishing Carleson measures.
We introduce potential spaces on fractal metric spaces, investigate their embedding theorems, and derive various Besov spaces. Our starting point is that there exists a local, stochastically complete heat kernel satisfying a two-sided estimate on the fractal considered.