L^p L p Fourier multipliers on compact Lie groups

2011/02/28 by Michael Ruzhansky, Jens Wirth · 63 citations
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Differential operator #Discrete mathematics #Fourier transform #Fundamental representation #Geometry #Hypoelliptic operator #Invariant (physics) #Lie algebra #Lie group #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematical physics #Mathematics #Maximal torus #Multiplier (economics) #Pure mathematics #Torus #math.AP #math.FA #math.RT #msc:22E30 #msc:43A15 #msc:43A22 #msc:43A77

paper · pdf · doi:10.1007/s00209-015-1440-9

published in Mathematische Zeitschrift 280(3-4), 621-642 (Springer Science+Business Media) · 22 pages; minor corrections

arxiv created 2015/01/05 · openalex publication_date 2015/03/07 · arxiv updated 2015/10/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this paper we prove L^p Fourier multiplier theorems for invariant and also non-invariant operators on compact Lie groups in the spirit of the well-known Hörmander–Mikhlin theorem on \mathbb Rⁿ and its variants on tori \mathbb Tⁿ . We also give applications to a-priori estimates for non-hypoelliptic operators. Already in the case of tori we get an interesting refinement of the classical multiplier theorem.

Citations

• Global Quantization of Pseudo-Differential Operators on Compact Lie Groups, SU(2), 3-sphere, and Homogeneous Spaces
• Hardy-Littlewood inequalities and Fourier multipliers on SU(2)
• Estimates for translation invariant operators in Lp spaces
• Sharp Gårding inequality on compact Lie groups
• Hörmander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity