ON THE LEFT LINEAR HILBERT PROBLEM IN CLIFFORD ANALYSIS

In this paper, we consider a Hilbert boundary value problem in R-0,R-m Clifford analysis. Find a R-0,R-m-valued left monogenic function u(x) in R-+(m,) which can extend continuously to R-0(m), whose positive boundary value u(+) satisfies X-(m) (a(t)u(+)(t)) = c(t), t is an element of R-0(m), where c(t) is a R-0,(m-1)-valued function, a(x) is a given R-0,R-m-valued function, whose inverse a(-1)(x) exsists. We may transform the Hilbert problem into a Riemann boundary value problem, in [1] the Riemann problem may be solved by the successive approximation, if a(x) satisfies some conditions.