Holder Norm Estimate for a Hilbert Transform in Hermitean Clifford Analysis

作者：Ricardo; ABREU-BLAYA; Juan; BORY-REYES...clifford分析希尔伯特变换范数估计hilbert变换连续循环r指数dgt变换域

摘要：A Hilbert transform for Hlder continuous circulant (2 × 2) matrix functions, on the d-summable (or fractal) boundary Γ of a Jordan domain Ω in R2n , has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the Hlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the Hlder exponents, the diameter of Γ and a specific d-sum (d > d) of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.

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