TY - JOUR
T1 - Hölder norm estimate for a Hilbert transform in Hermitean Clifford analysis
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
AU - Brackx, Fred
AU - de Schepper, Hennie
AU - Sommen, Frank
PY - 2012/11
Y1 - 2012/11
N2 - A Hilbert transform for Hölder continuous circulant (2 × 2) matrix functions, on the d-summable (or fractal) boundary Γ of a Jordan domain Ω in ℝ 2n, has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the Hölder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the Hölder 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.
AB - A Hilbert transform for Hölder continuous circulant (2 × 2) matrix functions, on the d-summable (or fractal) boundary Γ of a Jordan domain Ω in ℝ 2n, has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the Hölder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the Hölder 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.
KW - Hermitean Clifford analysis
KW - Hilbert transform
KW - fractal geometry
UR - http://www.scopus.com/inward/record.url?scp=84867329818&partnerID=8YFLogxK
U2 - 10.1007/s10114-012-0377-8
DO - 10.1007/s10114-012-0377-8
M3 - Artículo
SN - 1439-8516
VL - 28
SP - 2289
EP - 2300
JO - Acta Mathematica Sinica, English Series
JF - Acta Mathematica Sinica, English Series
IS - 11
ER -