| Abstrakt: |
Let Γ be a d-summable surface in R m , i.e., the boundary of a Jordan domain in R m , such that ∫ 0 1 N Γ (τ) τ d - 1 d τ < + ∞ , where N Γ (τ) is the number of balls of radius τ needed to cover Γ and m - 1 < d < m . In this paper, we consider a singular integral operator S Γ ∗ associated with the iterated equation D x ̲ k f = 0 , where D x ̲ stands for the Dirac operator constructed with the orthonormal basis of R m . The fundamental result obtained establishes that if α > d m , the operator S Γ ∗ transforms functions of the higher order Lipschitz class Lip (Γ , k + α) into functions of the class Lip (Γ , k + β) , for β = m α - d m - d . In addition, an estimate for its norm is obtained. [ABSTRACT FROM AUTHOR] |
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