A Hormander Type Multiplier Theorem on Fractional Fourier Multiplier Operators

Authors

  • Dan Li

Keywords:

Fractional Fourier multiplier, H¨ormander type multiplier theorem, Littlewood-Paley’s inequality.

Abstract

In this article, we consider the bilinear and biparameter fractional Fourier multiplier operators Tm, whose symbol m satisfies a certain H¨ormander type multiplier condition. We prove the boundedness of Tm on Lebesgue spaces. More precisely, we show that Tm is bounded from Lp1(R2n)×Lp2(R2n) to Lq(R2n) for appropriate indices p1,p2 and q. This is a bilinear-biparameter extension of the classical H¨ormander type multiplier theorem.

Key words and phrases. Fractional Fourier multiplier, H¨ormander type multiplier theorem, Littlewood-Paley’s inequality.

2000 Mathematics Subject Classification. 42B20

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Published

2025-05-18

How to Cite

Dan Li. (2025). A Hormander Type Multiplier Theorem on Fractional Fourier Multiplier Operators. Jordan Journal of Mathematics and Statistics, 10(2), 169–188. Retrieved from https://jjms.yu.edu.jo/index.php/jjms/article/view/1008

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Articles