Radial growth and Hardy-Littlewood-type theorems on hyperbolic harmonic functions

Hardy-Littlewood Theorems for A-Harmonic Tensors

Binary Additive Problems: Theorems of Landau and Hardy-littlewood Type

We prove theorems of Landau and Hardy-Littlewood type for Goldbach, Chen, Lemoime-Levy and other binary partitions of positive integers. We also pose some new conjectures.

Hardy-Littlewood and Caccioppoli-Type Inequalities for A-Harmonic Tensors

Harmonic Functions on the Real Hyperbolic Ball I : Boundary Values and Atomic Decomposition of Hardy Spaces

Abstract. In this article we study harmonic functions for the Laplace-Beltrami operator on the real hyperbolic space Bn. We obtain necessary and sufficient conditions for this functions and their normal derivatives to have a boundary distribution. In doing so, we put forward different behaviors of hyperbolic harmonic functions according to the parity of the dimension of the hyperbolic ball Bn. ...

Harmonic functions on hyperbolic graphs

We consider admissible random walks on hyperbolic graphs. For a given harmonic function on such a graph, we prove that asymptotic properties of non-tangential boundedness and non-tangential convergence are almost everywhere equivalent. The proof is inspired by the works of F. Mouton in the cases of Riemannian manifolds of pinched negative curvature and infinite trees. It involves geometric and ...