Resumen
Let Γ be an n-dimensional rectifiable Ahlfors-David regular surface in ℝn+1. Let u be a continuous ℝ0,n-valued function on Γ, where ℝ0,n is the Clifford algebra associated with ℝn. Then we prove that the Cliffordian Cauchy transform (CΓu)(x) := ∫Γ y-x̄/A n+1|y-x|n+1n(y)u(y)dℋn(y), x ∉ Γ, has continuous limit values on F if and only if the truncated integrals SΓ,εu(z):= ∫ Γ\{|y-z|≤ε} y-z̄/An+1|y-z| n+1n(y)(u(y) - u(z))dℋn(y) converge uniformly on Γ as ε → 0.
Idioma original | Inglés |
---|---|
Páginas (desde-hasta) | 167-178 |
Número de páginas | 12 |
Publicación | Zeitschrift fur Analysis und ihre Anwendung |
Volumen | 24 |
N.º | 1 |
Estado | Publicada - 2005 |
Publicado de forma externa | Sí |