Besov continuity of pseudo-differential operators on compact Lie groups revisited

Cardona, Duván

doi:10.1016/j.crma.2017.02.012

Harmonic analysis/Functional analysis

Besov continuity of pseudo-differential operators on compact Lie groups revisited
[Continuité de Besov des opérateurs pseudo-différentiels sur les groupes de Lie compacts revisitée]

Présenté par : the Editorial Board

Cardona, Duván ¹

¹ Mathematics Department, Universidad de los Andes, Carrera 1 No. 18a 10, Bogotá, Colombia

Comptes Rendus. Mathématique, Tome 355 (2017) no. 5, pp. 533-537.

Résumé
Abstract

Dans cette note, nous présentons quelques résultats sur l'action des opérateurs pseudo-différentiels globaux sur les espaces de Besov des groupes de Lie compacts.

In this note we present some results on the action of global pseudo-differential operators on Besov spaces on compact Lie groups.

Reçu le : 2016-10-29
Accepté le : 2017-02-28
Publié le : 2017-04-14

DOI : 10.1016/j.crma.2017.02.012

Affiliations des auteurs :

Cardona, Duván ¹

¹ Mathematics Department, Universidad de los Andes, Carrera 1 No. 18a 10, Bogotá, Colombia

@article{CRMATH_2017__355_5_533_0,
     author = {Cardona, Duv\'an},
     title = {Besov continuity of pseudo-differential operators on compact {Lie} groups revisited},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {533--537},
     publisher = {Elsevier},
     volume = {355},
     number = {5},
     year = {2017},
     doi = {10.1016/j.crma.2017.02.012},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2017.02.012/}
}

TY  - JOUR
AU  - Cardona, Duván
TI  - Besov continuity of pseudo-differential operators on compact Lie groups revisited
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 533
EP  - 537
VL  - 355
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2017.02.012/
DO  - 10.1016/j.crma.2017.02.012
LA  - en
ID  - CRMATH_2017__355_5_533_0
ER  -

%0 Journal Article
%A Cardona, Duván
%T Besov continuity of pseudo-differential operators on compact Lie groups revisited
%J Comptes Rendus. Mathématique
%D 2017
%P 533-537
%V 355
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2017.02.012/
%R 10.1016/j.crma.2017.02.012
%G en
%F CRMATH_2017__355_5_533_0

Cardona, Duván. Besov continuity of pseudo-differential operators on compact Lie groups revisited. Comptes Rendus. Mathématique, Tome 355 (2017) no. 5, pp. 533-537. doi : 10.1016/j.crma.2017.02.012. http://www.numdam.org/articles/10.1016/j.crma.2017.02.012/

Bibliographie
Cité par

[1] Akylzhanov, R.; Ruzhansky, M. Fourier multipliers and group von Neumann algebras, C. R. Acad. Sci. Paris, Ser. I, Volume 354 (2016), pp. 766-770

[2] Akylzhanov, R.; Nursultanov, E.; Ruzhansky, M. Hardy–Littlewood inequalities and Fourier multipliers on SU(2), Stud. Math., Volume 234 (2016), pp. 1-29

[3] Bourdaud, G. $L^{p}$ -estimates for certain non-regular pseudo-differential operators, Commun. Partial Differ. Equ., Volume 7 (1982), pp. 1023-1033

[4] Cardona, D. Besov continuity for multipliers defined on compact Lie groups, Palest. J. Math., Volume 5 (2016) no. 2, pp. 35-44

[5] Cardona, D.; Ruzhansky, M. Littlewood–Paley theorem, Nikolskii inequality, Besov spaces, Fourier and spectral multipliers on graded Lie groups | arXiv

[6] Delgado, J. $L^{p}$ bounds for pseudo-differential operators on the torus, Oper. Theory, Adv. Appl., Volume 231 (2012), pp. 103-116

[7] Delgado, J.; Ruzhansky, M. $L^{p}$ -bounds for pseudo-differential operators on compact Lie groups, J. Inst. Math. Jussieu (2017) | DOI

[8] Fefferman, C. $L^{p}$ -bounds for pseudo-differential operators, Isr. J. Math., Volume 14 (1973), pp. 413-417

[9] Fischer, V. Intrinsic pseudo-differential calculi on any compact Lie group, J. Funct. Anal., Volume 268 (2015) no. 11, pp. 3404-3477

[10] Fischer, V. Hörmander condition for Fourier multipliers on compact Lie groups | arXiv

[11] Gibbons, G. Operateurs pseudo-differentiels et espaces de Besov, C. R. Acad. Sci. Paris, Ser. A, Volume 286 (1978), pp. 895-897

[12] Hörmander, L. Estimates for translation invariant operators in $L^{p}$ spaces, Acta Math., Volume 104 (1960), pp. 93-140

[13] Hörmander, L. The Analysis of the Linear Partial Differential Operators, vol. III, Springer-Verlag, 1985

[14] Marcinkiewicz, J. Sur les multiplicateurs des séries de Fourier, Stud. Math., Volume 8 (1939), pp. 78-91

[15] Mihlin, S.G. On the multipliers of Fourier integrals, Dokl. Akad. Nauk SSSR (N.S.), Volume 109 (1956), pp. 701-703

[16] Nursultanov, E.; Ruzhansky, M.; Tikhonov, S. Nikolskii inequality and functional classes on compact Lie groups, Funct. Anal. Appl., Volume 49 (2015), pp. 226-229

[17] Nursultanov, E.; Ruzhansky, M.; Tikhonov, S. Nikolskii inequality and Besov, Triebel–Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds, Ann. Sc. Norm. Super. Pisa, Cl. Sci., Volume XVI (2016), pp. 981-1017

[18] Ruzhansky, M.; Turunen, V. Pseudo-Differential Operators and Symmetries: Background Analysis and Advanced Topics, Birkhäuser-Verlag, Basel, Switzerland, 2010

[19] Ruzhansky, M.; Turunen, V. Sharp Garding inequality on compact Lie groups, J. Funct. Anal., Volume 260 (2011), pp. 2881-2901

[20] Ruzhansky, M.; Turunen, V. Global quantization of pseudo-differential operators on compact Lie groups, SU(2) and 3-sphere, Int. Math. Res. Not. IMRN, Volume 2013 (2013) no. 11, pp. 2439-2496

[21] Ruzhansky, M.; Turunen, V.; Wirth, J. Hörmander class of pseudo-differential operators on compact Lie groups and global hypoellipticity, J. Fourier Anal. Appl., Volume 20 (2014), pp. 476-499

[22] Ruzhansky, M.; Wirth, J. On multipliers on compact Lie groups, Funct. Anal. Appl., Volume 47 (2013), pp. 72-75

[23] Ruzhansky, M.; Wirth, J. Global functional calculus for operators on compact Lie groups, J. Funct. Anal., Volume 267 (2014) no. 1, pp. 144-172

[24] Ruzhansky, M.; Wirth, J. $L^{p}$ Fourier multipliers on compact Lie groups, Math. Z., Volume 280 (2015) no. 3–4, pp. 621-642

Cité par Sources :