Extreme harmonic functions on a ball

A Class of Extreme X-harmonic Functions

Salisbury and Verzani introduced a class of martingales for the Brownian superprocess related to conditionings of the process to exit the boundary of a bounded domain in Rd in a particular way. The corresponding class of functions, denoted Hg,h1,...,hN , was generalized by Dynkin to more general superprocesses and shown to be X-harmonic. Salisbury and Verzani conjectured that a certain choice o...

A lower estimate of harmonic functions

We shall give a lower estimate of harmonic‎ ‎functions of order greater than one in a half space‎, ‎which‎ ‎generalize the result obtained by B‎. ‎Ya‎. ‎Levin in a half plane‎.

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. ...

On the Monotonicity of Positive Invariant Harmonic Functions in the Unit Ball

A monotonicity property of Harnack inequality is proved for positive invariant harmonic functions in the unit ball.

More on Harmonic Functions