By H. Cartan

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When ω ∈ Mθ , the composite function fkl and its continuous mixed partial derivatives up to order m for different z j (j = l) are uniformly bounded, we denote its bound by Kθ .

7 are generalizations of those in [19]. CHAPTER II BOUNDARY VALUE PROBLEMS OF GENERALIZED REGULAR FUNCTIONS AND HYPERBOLIC HARMONIC FUNCTIONS IN REAL CLIFFORD ANALYSIS This chapter deals with boundary value problems of some functions in real Clifford analysis. In the first three sections, the problems of regular and generalized regular functions are considered, and in the last section, the Dirichlet problem of hyperbolic harmonic functions is discussed. Most results in this chapter have been obtained by us in recent years.

5). , l2n−1 . 30) ωA (x)eA , x ∈ Ω. The following assumption is called the condition V . , 2n−2 . , zm . , m. , ζm ) N1 = f . , λ. , 2n−2 , 1 ≤ j, l ≤ m. ∂z i1 iλ ⎪ ⎪ ⎩ ⎭ 1 ≤ i1 < · · · < iλ ≤ m, 1 ≤ λ ≤ m, z ∈ Ω is defined. When ω ∈ Mθ , the composite function fkl and its continuous mixed partial derivatives up to order m for different z j (j = l) are uniformly bounded, we denote its bound by Kθ .

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