On the Harnack inequality for antisymmetric s-harmonic functions

Monotonicity of Harnack Inequality for Positive Invariant Harmonic Functions

Boundary Harnack Inequality for Α-harmonic Functions on the Sierpiński Triangle

The analysis and probability theory on fractals underwent rapid development in last twenty years, see [1, 11, 27, 28] and the references therein. Diffusion processes were constructed for the Sierpiński triangle [4, 15, 21] and more generally for some simple nested fractals [17] and Sierpiński carpets [2, 18, 20, 22]. In [25] Stós introduced a class of subordinate processes on d-sets, called α-s...

Harnack ’ s inequality for some nonlocal equations and application

In this paper, we establish a Harnack’s inequality for positive solutions of the nonlocal inhomogeneous problem

Harnack Inequality on Homogeneous Spaces

We consider a connected, locally compact topological space X. We suppose that a pseudo-distance d is defined on X that is, d : X × X 7−→ R+ such that d (x, y) > 0 if and only if x 6= y; d (x, y) = d (y, x) ; d (x, z) ≤ γ [d (x, y) + d (y, z)] for all x, y, z ∈ X, where γ ≥ 1 is some given constant and we suppose that the pseudo-balls B (x, r) = {y ∈ X : d (x, y) < r} , r > 0, form a basis of op...

Boundary Harnack principle and elliptic Harnack inequality

We prove a scale-invariant boundary Harnack principle for inner uniform domains over a large family of Dirichlet spaces. A novel feature of our work is that our assumptions are robust to time changes of the corresponding diffusions. In particular, we do not assume volume doubling property for the symmetric measure.