Abstract
We adapt a technique developed by Bojarski and Iwaniec in their celebrated 1983 paper [2] to prove second order differentiability results for $p$-harmonic functions to the case of the Heisenberg group. We prove that for $2\le p<4$ we have $X_i ( |Xu|^{(p-2)/p}\, X_j u) \in L^2_{\rm loc} (\Omega )$ and $X_i (|Xu|^p ) \in L^2_{\rm loc} (\Omega)$, where $u$ is a $p$-harmonic function in the Heisenberg group $\mathbb{H}^n$.
Citation
Andràs Domokos. Juan J. Manfredi. "A second order differentiability technique of Bojarski-Iwaniec in the Heisenberg group." Funct. Approx. Comment. Math. 40 (1) 69 - 74, March 2009. https://doi.org/10.7169/facm/1238418798
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