A multi-parameter family of Fourier integral operators
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912726760030208 |
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| author | Dou, Mengmeng Wang, Zipeng Zhang, Jiashu |
| author_facet | Dou, Mengmeng Wang, Zipeng Zhang, Jiashu |
| contents | We study a new class of Fourier integral operators defined in R^N. Their symbols are allowed to satisfy a differential inequality with certain multi-parameter characteristic. We prove these operators of order -(N-1)/2
bounded from the classical, atom decomposable H^1-Hardy space to L^1(R^N). As a result, we obtain a sharp L^p-estimate.
Simultaneously, a generalized Sobolev Lp-space is introduced. We establish the Sobolev Lp-norm inequality for convolutions with a distribution having singularity on the unit sphere. As an application, we give a new a priori estimate for the solution of wave equations by requiring less regularity on the source term and initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07781 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A multi-parameter family of Fourier integral operators Dou, Mengmeng Wang, Zipeng Zhang, Jiashu Classical Analysis and ODEs We study a new class of Fourier integral operators defined in R^N. Their symbols are allowed to satisfy a differential inequality with certain multi-parameter characteristic. We prove these operators of order -(N-1)/2 bounded from the classical, atom decomposable H^1-Hardy space to L^1(R^N). As a result, we obtain a sharp L^p-estimate. Simultaneously, a generalized Sobolev Lp-space is introduced. We establish the Sobolev Lp-norm inequality for convolutions with a distribution having singularity on the unit sphere. As an application, we give a new a priori estimate for the solution of wave equations by requiring less regularity on the source term and initial data. |
| title | A multi-parameter family of Fourier integral operators |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2410.07781 |