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Higher order Riesz transforms for Hermite expansions
1College of Sciences, North China University of Technology, Beijing, 100144 China.
Journal of Inequalities and Applications
|May 23, 2017
Summary
This study analyzes higher-order Riesz transforms linked to the harmonic oscillator and Hermite functions. We prove the boundedness of these transforms on the Hardy space, advancing harmonic analysis research.
Area of Science:
- Harmonic analysis
- Functional analysis
- Partial differential equations
Background:
- The Riesz transform is a fundamental operator in harmonic analysis.
- Understanding its properties for higher orders and specific potentials like the harmonic oscillator is crucial.
- The Hardy space is a key function space in analysis.
Purpose of the Study:
- To investigate the Riesz transform of higher order associated with the harmonic oscillator.
- To establish the boundedness of these operators on the Hardy space.
Main Methods:
- Utilizing techniques from harmonic analysis.
- Applying methods related to the Laplacian and Hermite functions.
- Leveraging properties of the Hardy space.
Main Results:
- The Riesz transform of higher order associated with the harmonic oscillator is considered.
- The boundedness of these Riesz transforms on the Hardy space is proven.
Conclusions:
- The study successfully demonstrates the boundedness of higher-order Riesz transforms for the harmonic oscillator on the Hardy space.
- This contributes to the understanding of Riesz transforms in the context of special functions and function spaces.
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