Let R0,n be the real Clifford algebra generated by e1, e2, … , en satisfying eiej +ejei = −2δij , i, j = 1, 2, … , n. e0 is the unit element. Let Ω be an open set. A function f is called left generalized analytic in Ω if f satisfies the equation
Lf = 0, (0.1)
where
L = q0e0∂x0 + q1e1∂x1 + … + qnen∂xn,
qi > 0, i = 0, 1, … , n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in Rn+1+ will be investigated.