HW^2,2_loc-regularity for p-harmonic functions in Heisenberg groups

Let 1 < p ≤ 4 {1<p\leq 4} when n = 1 {n=1}, and 1 < p < 3 + 1 n - 1 {1<p<3+\frac{1}{n-1}} when n ≥ 2 {n\geq 2}. We obtain the second-order horizontal Sobolev HW loc 2, 2 {\operatorname{HW}{2,2}{\mathrm{loc}}} -regularity of p-harmonic functions in the Heisenberg group n {{\mathbb{H}}{n}}. This improves the known range of p obtained by Domokos and Manfredi in 2005.