Besov continuity for global operators on compact Lie groups: the critical case $p=q=\infty.$

TL;DR

This paper investigates the boundedness of certain global pseudo-differential operators on Besov spaces over compact Lie groups, focusing on the critical case where p=q=∞, under limited regularity conditions.

Contribution

It extends the understanding of operator mapping properties to the critical case p=q=∞ on Besov spaces with limited regularity symbols.

Findings

Established boundedness of operators on B^{s}_{ ext{∞,∞}}(G)

Extended previous results to the critical p=q=∞ case

Analyzed symbols satisfying Fefferman type conditions

Abstract

In this note, we study the mapping properties of global pseudo-differential operators with symbols in Ruzhansky-Turunen classes on Besov spaces $B^{s}_{\infty,\infty}(G).$ The considered classes satisfy Fefferman type conditions of limited regularity.