Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/l-p-l-p-fourier-multipliers-on-compact-lie-groups-tdHMnDpuKY
References (19)
-
MV Ruzhansky, J Wirth (2013)
On multipliers on compact Lie groupsFunct. Anal. Appl., 47
-
M Ruzhansky, J Wirth (2014)
Global functional calculus for operators on compact Lie groupsJ. Funct. Anal., 267
-
R Coifman, G Weiss (1971)
Analyse Harmonique Non-Vommutative Sur Certains Espaces Homogenes, Lecture Notes in Mathematics -
M Ruzhansky, V Turunen (2010)
Quantization of pseudo-differential operators on the torusJ. Fourier Anal. Appl., 16
-
EM Stein (1970)
Topics in Harmonic Analysis Related to the Littlewood–Paley Theory, vol. 63 of Annals of Mathematics Studies -
HD Fegan (1991)
Introduction to Compact Lie Groups, Series in Pure Mathematics -
G Alexopoulos (1994)
Spectral multipliers on Lie groups of polynomial growthProc. Am. Math. Soc., 120
-
R Coifman, G Weiss (1970)
Multiplier transformations of functions on $${\rm SU}(2)$$ SU ( 2 ) and $$\Sigma _2$$ Σ 2Rev. Un. Mat. Argent., 25
-
R Coifman, M Guzman (1970)
Singular integrals and multipliers on homogeneous spacesRev. Un. Mat. Argent., 25
-
M Ruzhansky, V Turunen (2007)
On the Fourier analysis of operators on the torus, modern trends in pseudo-differential operatorsOper. Theory Adv. Appl., 172
-
M Ruzhansky, V Turunen, J Wirth (2014)
Hörmander class of pseudo-differential operators on compact Lie groups and global hypoellipticityJ. Fourier Anal. Appl., 20
-
R Coifman, G Weiss (1973)
Central multiplier theorems for compact Lie groupsBull. Am. Math. Soc., 80
-
M Ruzhansky, V Turunen (2010)
Pseudo-Differential Operators and Symmetries -
J-P Anker (1990)
$$L_p$$ L p Fourier multipliers on Riemannian symmetric spaces of the noncompact typeAnn. of Math., 132
-
M Ruzhansky, V Turunen (2011)
Sharp Gårding inequality on compact Lie groupsJ. Funct. Anal., 260
-
M Cowling (1983)
Harmonic analysis on semigroupsAnn. Math., 117
-
L Hörmander (1960)
Estimates for translation invariant operators in $$L^{p}$$ L p spacesActa Math., 104
-
M Cowling, A Sikora (2001)
A spectral multiplier theorem for a sublaplacian on SU(2)Math. Z., 238
-
SM Nikolskii (1977)
Approximation of functions of several variables and imbedding theorems (Russian)
- Publisher
- Springer Journals
- Copyright
- Copyright © 2015 by The Author(s)
- Subject
- Mathematics; Mathematics, general
- ISSN
- 0025-5874
- eISSN
- 1432-1823
- DOI
- 10.1007/s00209-015-1440-9
- Publisher site
- See Article on Publisher Site
Abstract
In this paper we prove $$L^p$$ 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 $$\mathbb R^n$$ R n and its variants on tori $$\mathbb T^n$$ T n . 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.
Journal
Mathematische Zeitschrift – Springer Journals
Published: Mar 8, 2015