Lipschitz classes of A-harmonic functions in Carnot groups

Growth of A-Harmonic Functions and Carnot Groups

The order of growth of a harmonic function is determined by the growth of its gradient and conversely. We extend these results to solutions of certain subelliptic equations in John domains in Carnot groups. The modulus of the gradient is replaced by a local average of the horizontal gradient. In the harmonic case these quantities are equivalent. The proof uses recent integral inequalities assoc...

ON THE REGULARITY OF SUBELLIPTIC p-HARMONIC FUNCTIONS IN CARNOT GROUPS

In this paper we prove second order horizontal differentiability and C1,α regularity results for subelliptic p-harmonic functions in Carnot groups for p close to 2.

On a linear combination of classes of harmonic $p-$valent functions defined by certain modified operator

In this paper we obtain coefficient characterization‎, ‎extreme points and‎ ‎distortion bounds for the classes of harmonic $p-$valent functions‎ ‎defined by certain modified operator‎. ‎Some of our results improve‎ ‎and generalize previously known results‎.

Extending Functions in the Model Subspaces of H^2(R) to C

CHARACTERIZATION BY ASYMPTOTIC MEAN FORMULAS OF q−HARMONIC FUNCTIONS IN CARNOT GROUPS

Aim of this paper is to extend the work [9] to the Carnot group setting. More precisely, we prove that in every Carnot group a function is q−harmonic (here 1 < q < ∞), if and only if it satisfies a particular asymptotic mean value formula.