Boundedness of pseudo-differential operators in subelliptic Sobolev and Besov spaces on compact Lie groups

References

• Delgado J, Ruzhansky M. Lp-bounds for pseudo-differential operators on compact Lie groups. J Inst Math Jussieu. 2019;18(3):531–559.
   Web of Science ®Google Scholar
• Ruzhansky M, Wirth J. Lp Fourier multipliers on compact Lie groups. Math Z. 2015;280:621–642.
   Web of Science ®Google Scholar
• Ruzhansky M, Wirth J. Global functional calculus for operators on compact Lie groups. J Funct Anal. 2014;267:144–172.
   Web of Science ®Google Scholar
• Stein E. On some functions of Littlewood–Paley and Zygmund. Bull Amer Math Soc. 1961;67:99–101.
   Web of Science ®Google Scholar
• Taibleson MH. On the theory of Lipschitz spaces of distributions on Euclidean n-space: I. J Math Mech. 1964;13:407–479. II. ibid. 1965;14:821–839. III. ibid. 1966;15:973–981.
   Web of Science ®Google Scholar
• Besov OV. On a family of function spaces. Embeddings theorems and applications [in Russian]. Dokl Akad Nauk SSSR. 1959;126:1163–1165.
   Google Scholar
• Besov OV. On a family of function spaces in connection with embeddings and extensions, [in Russian] trudy. Mat Inst Steklov. 1961;60:42–81.
   Google Scholar
• Peetre J. Sur les espaces de Besov. C R Acad Sci Paris. 1967;264:281–283.
   Google Scholar
• Peetre J. Remarques sur les espaces de Besov. Le case 0<p<1. C R Acad Sci Paris. 1973;277:947–950.
   Google Scholar
• Triebel H. Theory of function spaces. Basel: Birkhäuser Verlag; 1983. (Monographs in Mathematics; vol. 78).
   Google Scholar
• Triebel H. Theory of function spaces. III. Basel: Birkhäuser Verlag; 2006. (Monographs in Mathematics; vol. 100).
   Google Scholar
• Nursultanov E, Ruzhansky M, Tikhonov S. Nikolskii inequality and functional classes on compact Lie groups. Funct Anal Appl. 2015;49:226–229.
   Google Scholar
• Nursultanov E, Ruzhansky M, Tikhonov S. Nikolskii inequality and Besov, Triebel-Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds. Ann Sci Norm Super Pisa Cl Sci. 2016;16:981–1017.
   Google Scholar
• Fefferman C. Lp-bounds for pseudo-differential operators. Israel J Math. 1973;14:413–417.
   Web of Science ®Google Scholar
• Rothschild LP, Stein EM. Hypoelliptic differential operators and nilpotent groups. Acta Math. 1976;137(3-4):247–320.
   Web of Science ®Google Scholar
• Garetto C. Lp and Sobolev boundedness of pseudodifferential operators with non-regular symbol: a regularisation approach. J Math Anal Appl. 2011;381:328–343.
   Web of Science ®Google Scholar
• Cardona D, Delgado J, Ruzhansky M. Lp-bounds for pseudo-differential operators on graded Lie groups. arXiv:1911.03397.
   Google Scholar
• Cardona D. Besov continuity for Multipliers defined on compact Lie groups. Palest J Math. 2016;5(2):35–44.
   Google Scholar
• Cardona D. Besov continuity of pseudo-differential operators on compact Lie groups revisited. C R Math Acad Sci Paris. 2017;355(5):533–537.
   Google Scholar
• Cardona D. Continuity of pseudo-differential operators on Besov spaces on compact homogeneous manifolds. J Pseudo-Differ Oper Appl. 2018;9(4):861–880.
   Web of Science ®Google Scholar
• Calderon AP, Vaillancourt R. On the boundedness of pseudo-differential operators. J Math Soc Jpn. 1971;23(2):374–378.
   Web of Science ®Google Scholar
• Fischer V. Intrinsic pseudo-differential calculi on any compact Lie group. J Funct Anal. 2015;268:3404–3477.
   Web of Science ®Google Scholar
• Li CZ, Wang RH. On the Lp-boundedness of several classes of pseudo-differential operators. Chinese Ann Math. 1984;5:193–213.
   Web of Science ®Google Scholar
• Park B. On the boundedness of Pseudo-differential operators on Triebel–Lizorkin and Besov spaces. J Math Anal Appl. 2018;1:544–576.
   Google Scholar
• Delgado J. Estimations Lp pour une classe d' operateurs pseudo-differentiels dans le cadre du calcul de Weyl–Hörmander. J Anal Math. 2006;100:337–374.
   Web of Science ®Google Scholar
• Delgado J. Lp bounds in S(m,g)-calculus. Complex Var Elliptic Equations. 2015;61(3):315–337.
   Web of Science ®Google Scholar
• Ruzhansky M, Turunen V. Pseudo-differential operators and symmetries: background analysis and advanced topics. Basel: Birkhäuser-Verlag; 2010.
   Google Scholar
• Hörmander L. Hypoelliptic second order differential equations. Acta Math. 1967;119:147–171.
   Web of Science ®Google Scholar
• Hassannezhad A, Kokarev G. Sub-Laplacian eigenvalue bounds on sub-Riemannian manifolds. Ann Scuola Norm Sup Pisa Cl Sci. 2016;16(4):1049–1092.
   Google Scholar
• Bahouri H, Chemin JY, Danchin R. Basic analysis. In: Fourier analysis and nonlinear partial differential equations: Grundlehren der mathematischen wissenschaften. vol. 343, Berlin, Heidelberg: Springer, 2011.
   Google Scholar
• Akylzhanov R, Ruzhansky M. Lp−Lq multipliers on locally compact groups. J Funct Anal. 2020;278(3):108324.
   Web of Science ®Google Scholar
• Brezis H. Analyse fonctionnelle: théorie et applications. In: Ciarlet PG, Lions JL, editors. Collection Mathématiques appliquées pour la maîtrise. Dunod; 1999.
   Google Scholar
• Garetto C, Ruzhansky M. Wave equation for sum of squares on compact Lie groups. J Differ Equations. 2015;258:4324–4347.
   Web of Science ®Google Scholar
• Furioli G, Melzi C, Veneruso A. Littlewood–Paley decompositions and Besov spaces on Lie groups of polynomial growth. Math Nachr. 2006;279(9-10):1028–1040.
   Web of Science ®Google Scholar
• Fischer V. Differential structure on the dual of a compact Lie group, arXiv:1610.06348.
   Google Scholar
• Ruzhansky M, Turunen V. Global quantization of pseudo-differential operators on compact Lie groups, SU(2) and 3-sphere. Int Math Res Not IMRN. 2013;11:2439–2496.
   Google Scholar
• Ruzhansky M. Hörmander class of pseudo-differential operators on compact Lie groups and global hypoellipticity. J Fourier Anal Appl. 2014;20:476–499.
   Web of Science ®Google Scholar
• Weidmann J. Linear operators in Hilbert spaces. New York-Berlin: Springer-Verlag; 1980. (Graduate Texts in Mathematics; vol. 68). Translated from the German by Joseph Szücs.
   Google Scholar
• Cardona D. Nuclear pseudo-differential operators in Besov spaces on compact Lie groups. J Fourier Anal Appl. 2017;23(5):1238–1262.
   Web of Science ®Google Scholar
• Cardona D, Ruzhansky M. Multipliers for Besov spaces on graded Lie groups. C R Math Acad Sci Paris. 2017;355(4):400–405.
   Google Scholar
• Fischer V, Ruzhansky M. Sobolev spaces on graded groups. Ann Inst Fourier. 2017;67:1671–1723.
   Web of Science ®Google Scholar
• Bahouri H, Gérard P, Xu C-J. Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg. J Anal Math. 2000;82:93–118.
   Web of Science ®Google Scholar