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Hölder norm estimate for the fractal Hilbert transform in Douglis analysis.
Yudier Peña Pérez1, Martín P Árciga Alejandre1, Ricardo Abreu Blaya2
1Facultad de Matemática, Universidad Autónoma de Guerrero, Avenida Lázaro Cárdenas sn, Chilpancingo, Guerrero 39087 México.
Journal of Inequalities and Applications
|September 29, 2017
Summary
This study estimates the Hölder norm for a fractal Hilbert transform within Douglis analysis. The research focuses on functions defined on h-summable curves, advancing fractal analysis and operator theory.
Area of Science:
- Harmonic Analysis
- Fractal Geometry
- Functional Analysis
Background:
- The Hilbert transform is a fundamental operator in harmonic analysis.
- Fractal analysis extends classical concepts to irregular geometric objects.
- Douglis analysis provides a framework for studying operators on specific function spaces.
Purpose of the Study:
- To estimate the Hölder norm of a fractal Hilbert transform.
- To analyze the transform's action on Hölder spaces of functions with values in a Douglis algebra.
- To investigate the behavior of this transform on h-summable curves.
Main Methods:
- Utilizing techniques from harmonic analysis and fractal geometry.
- Applying concepts from Douglis analysis.
- Estimating norms of operators acting on function spaces.
Main Results:
- Successful estimation of the Hölder norm for the fractal Hilbert transform.
- Characterization of the transform's boundedness properties in the specified context.
Conclusions:
- The study provides a rigorous analysis of a fractal version of the Hilbert transform.
- Findings contribute to the understanding of operator theory in fractal settings.
- The results have implications for the analysis of functions on complex, irregular domains.
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