The rational Dunkl operators are commuting differential-reflection operators on the Euclidean space R d associated with a root system. The aim of the paper is to study local boundary behaviour of generalized harmonic functions associated with the Dunkl operators. We introduce a Lusin-type area integral operator S by means of Dunkl's generalized translation and the Dunkl operators. The main results are on characterizations of local existence of non-tangential boundary limits of a generalized harmonic function u in the upper half-space R d+1 + associated with the Dunkl operators, and for a subset E of R d invariant under the reflection group generated by the root 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 ∈ E; (ii) u is non-tangentially bounded for a.e. x ∈ E; (iii) (Su)(x) is finite for a.e. x ∈ E.
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