Regularity of Fourier integrals on product spaces
Abstract
We study a family of Fourier integral operators by allowing their symbols to satisfy a multi-parameter differential inequality on R^N. We show that these operators of order -(N-1)/2 are bounded from classical, atom decomposable H^1-Hardy space to L^1(R^N). Consequently, we obtain a sharp L^p-regularity result due to Seeger, Sogge and Stein.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.09691
- arXiv:
- arXiv:2408.09691
- Bibcode:
- 2024arXiv240809691T
- Keywords:
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- Mathematics - Classical Analysis and ODEs
- E-Print:
- We corrected some typos and errors from the previous version