Hormander-Mikhlin type theorem on non-commutative spaces
Operator Algebras
2026-03-10 v2 Quantum Algebra
Abstract
In this paper, we introduce a Fourier-type formalism on non-commutative spaces. As a result, we obtain two versions of Hormander-Mikhlin Lp-multiplier theorem: on locally compact Kac groups and on semi-finite von Neumann algebras, respectively. In the simplest case our result coincides with a sharp version of the classical Hormander Lp-multiplier theorem, which was obtained by Grafakos and Slavikova in [11]. Finally, we present some applications to the evolution equation in non-commutative setting.
Cite
@article{arxiv.2503.01240,
title = {Hormander-Mikhlin type theorem on non-commutative spaces},
author = {Rauan Akylzhanov and Michael Ruzhansky and Kanat Tulenov},
journal= {arXiv preprint arXiv:2503.01240},
year = {2026}
}
Comments
24 pages