A note on $L^p$-$L^q$ boundedness of Fourier multipliers on noncommutative spaces

Abstract

In this work, we study Fourier multipliers on noncommutative spaces. In particluar, we show a simple proof of $L^p$-$L^q$ estimate of Fourier multipliers on general noncommutative spaces associated with semi-finite von Neumann algebras. This includes the case of Fourier multipliers on general locally compact unimodular groups.

arXiv commentMuch more improved than the previous version. In particular, the Fourier structure was corrected

References in corpus (4)

• $L^p$-$L^q$ boundedness of $(k,a)$-Fourier multipliers with applications to Nonlinear equations
• Fourier multiplier theorems involving type and cotype
• Smooth dense subalgebras and Fourier multipliers on compact quantum groups
• Expansion in generalized eigenfunctions for Laplacians on graphs and metric measure spaces

Cited by in corpus (2)

• $L^p-L^q$ boundedness of Fourier multipliers on quantum Euclidean spaces
• Hörmander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications