A Hilbert transform for H61der continuous circulant （2 × 2） matrix functions, on the d- summable （or fractal） boundary F of a Jordan domain Ω in R2n, has recently been introduced within the framework of Herm...A Hilbert transform for H61der continuous circulant （2 × 2） matrix functions, on the d- summable （or fractal） boundary F 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 HSlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the HSlder exponents, the diameter of F 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.展开更多
In recent papers by Brackx, Delanghe and Sommen, some fundamental higher dimensional distributions have been reconsidered in the framework of Clifford analysis, eventually leading to the introduction of four broad cla...In recent papers by Brackx, Delanghe and Sommen, some fundamental higher dimensional distributions have been reconsidered in the framework of Clifford analysis, eventually leading to the introduction of four broad classes of new distributions in Euclidean space. In the current paper we continue the in-depth study of these distributions, more specifically the study of their behaviour in frequency space, thus extending classical results of harmonic analysis.展开更多
文摘A Hilbert transform for H61der continuous circulant （2 × 2） matrix functions, on the d- summable （or fractal） boundary F 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 HSlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the HSlder exponents, the diameter of F 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.
文摘In recent papers by Brackx, Delanghe and Sommen, some fundamental higher dimensional distributions have been reconsidered in the framework of Clifford analysis, eventually leading to the introduction of four broad classes of new distributions in Euclidean space. In the current paper we continue the in-depth study of these distributions, more specifically the study of their behaviour in frequency space, thus extending classical results of harmonic analysis.
