Hölder Continuity and Boundedness Estimates for Nonlinear Fractional Equations in the Heisenberg Group

Abstract We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is fractional p -Laplacian operator on Heisenberg-Weyl group $$\mathbb {H}^n$$ H n . Among other results, we prove that weak solutions such problems are bounded and Hölder continuous, also establishing general estimates as Caccioppoli-type with tail logarithmic-type estimates.