BMO spaces associated with semigroups of operators

TL;DR

This paper investigates BMO spaces linked to operator semigroups, establishing a universal interpolation theorem and demonstrating the boundedness of Fourier multipliers on noncommutative Lp spaces with optimal constants.

Contribution

It introduces a universal interpolation theorem for BMO spaces associated with semigroups and proves boundedness of Fourier multipliers on noncommutative Lp spaces.

Findings

Established a universal interpolation theorem for BMO spaces.

Proved boundedness of Fourier multipliers on noncommutative Lp spaces.

Achieved optimal constants in p for these boundedness results.

Abstract

We study BMO spaces associated with semigroup of operators and apply the results to boundedness of Fourier multipliers. We prove a universal interpolation theorem for BMO spaces and prove the boundedness of a class of Fourier multipliers on noncommutative Lp spaces for all 1 < p < \infty, with optimal constants in p.