| Citation: |
Shaoguang Shi, Zunwei Fu, Qingyan Wu. ON THE AVERAGE OPERATORS, OSCILLATORY INTEGRALS, SINGULAR INTEGRALS AND THEIR APPLICATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 334-378. doi: 10.11948/20230225
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ON THE AVERAGE OPERATORS, OSCILLATORY INTEGRALS, SINGULAR INTEGRALS AND THEIR APPLICATIONS
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Abstract
This paper is a survey on three types of integral operators and their applications based on the research work of the authors and their cooperators in the recent decade. The first type is the average operator, including Hardy operators, Hausdorff operators and Hardy-Littlewood maximal operators. The second is the oscillatory type integral operator, such as one-sided oscillatory integral operators, Fourier transforms, fractional Fourier transforms and linear canonical transforms. The third type is the singular integral operators, including Hilbert transform, Riesz transforms, Cauchy type operators, etc. We mainly investigate their norm estimations, boundedness, weighted estimations, compactness characterizations and their properties in various function spaces.
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Keywords:
- Average operator /
- oscillatory integral /
- singular integral /
- function space
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References
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Shaoguang Shi, Zunwei Fu, Qingyan Wu. ON THE AVERAGE OPERATORS, OSCILLATORY INTEGRALS, SINGULAR INTEGRALS AND THEIR APPLICATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 334-378. doi: 10.11948/20230225
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