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The rational Dunkl operators are commuting differential-reflection operatorson the Euclidean space $\RR^d$ associated with a root system. The aim of thepaper is to study local boundary behaviour of generalized harmonic functionsassociated with the Dunkl operators. We introduce a Lusin-type area integraloperator $S$ by means of Dunkl's generalized translation and the Dunkloperators. The main results are on characterizations of local existence ofnon-tangential boundary limits of a generalized harmonic function $u$ in theupper half-space $\RR^{d+1}_+$ associated with the Dunkl operators, and for asubset $E$ of $\RR^d$ invariant under the reflection group generated by theroot system, the equivalence of the following three assertions are proved: (i)$u$ has a finite non-tangential limit at $(x,0)$ for a.e. $x\in E$; (ii) $u$ isnon-tangentially bounded for a.e. $x\in E$; (iii) $(Su)(x)$ is finite for a.e.$x\in E$.

Local boundary behaviour and the area integral of generalized harmonic functions associated with root systems