Hölder norm estimate for the fractal Hilbert transform in Douglis analysis

Abstract

Abstract The main goal of this paper is to estimate the Hölder norm of a fractal version of the Hilbert transform in the Douglis analysis context acting from Hölder spaces of Douglis algebra valued functions defined on h-summable curves.

Keywords

• hyperanalytic functions
• fractal dimensions
• Whitney decomposition
• Hilbert transform
• Hölder functions
• h-summables curves