Regularity theory for nonlocal equations with general growth in the Heisenberg group

Abstract: We deal with a wide class of generalized nonlocal $p$-Laplace equations, so-called nonlocal $G$-Laplace equations, in the Heisenberg framework. Under natural hypotheses on the $N$-function $G$, we provide a unified approach to investigate in the spirit of De Giorgi-Nash-Moser theory, some local properties of weak solutions to such kind of problems, involving boundedness, H\"{o}lder continuity and Harnack inequality. To this end, an improved nonlocal Caccioppoli-type estimate as the main auxiliary ingredient is exploited several times.