L²-L^p estimates and Hilbert–Schmidt pseudo differential operators on the Heisenberg motion group

References

• Kohn JJ, Nirenberg L. An algebra of pseudo-differential operators. Comm Pure Appl Math. 1965;18:269–305.
   Web of Science ®Google Scholar
• Hörmander L. The analysis of linear partial differential operators. III. Berlin: Springer-Verlag; 1985.
   Google Scholar
• Fischer V, Ruzhansky M. Quantization on nilpotent lie groups, progress in mathematics. Vol. 314. Basel: Birkhäuser; 2016.
   Google Scholar
• Ruzhansky M, Turunen V. Pseudo-differential operators and symmetries: background analysis and advanced topics. Basel: Birkhäuser-Verlag; 2010.
   Google Scholar
• Cardona D, Kumar V. Multilinear analysis for discrete and periodic pseudo-differential operators in Lp spaces. Rev Integr Temas Mat. 2018;36(2):151–164.
   Google Scholar
• Cardona D, Kumar V. Lp-boundedness and Lp-nuclearity of multilinear pseudo-differential operators on Zn and the torus Tn. J Fourier Anal Appl. 2019;25:2973–3017.
   Web of Science ®Google Scholar
• Cardona D, Kumar V. The nuclear trace of periodic vector-valued pseudo-differential operators with applications to index theory. Math Nachr. 2021;294:1657–1683.
   Web of Science ®Google Scholar
• Dasgupta A, Kumar V. Hilbert–Schmidt and trace class pseudo-differential operators on the abstract heisenberg group. J Math Anal Appl. 2020;486(12):14 pp., Article ID 123936.
   Google Scholar
• Fischer V, Ruzhansky M. A pseudo-differential calculus on the heisenberg group. C R Math Acad Sci Paris. 2014;352(3):197–204.
   Web of Science ®Google Scholar
• Kumar V. Pseudo-differential operators on homogeneous spaces of compact and hausdorff groups. Forum Math. 2019;31(2):275–282.
   Web of Science ®Google Scholar
• Kumar V, Mondal SS. Schatten class and nuclear pseudo-differential operators on homogeneous spaces of compact groups. Monatsh Math. 2022;197:149–176.
   Web of Science ®Google Scholar
• Wong MW. An introduction to pseudo-differential operators. 3rd ed. Singapore: World Scientific; 2014.
   Google Scholar
• Mantoiu M, Ruzhansky M. Pseudo-differential operators, wigner transform and weyl systems on type I locally compact groups. Doc Math. 2017;22:1539–1592.
   Web of Science ®Google Scholar
• Mantoiu M, Ruzhansky M. Quantizations on nilpotent Lie groups and algebras having flat coadjoint orbits. J Geom Anal. 2019;29(3):2823–2861.
   Web of Science ®Google Scholar
• Cardona D. On the boundedness of periodic pseudo-differential operators. Monatsh Math. 2018;185:189–206.
   Web of Science ®Google Scholar
• Dasgupta A, Wong MW. Pseudo-differential operators on the affine group in pseudo-differential operators: groups, geometry and applications. trends in mathematics. Cham; Birkhäuser: 2017.
   Google Scholar
• 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
• Delgado J, Ruzhansky M. Lp-nuclearity, traces, and grothendieck-Lidskii formula on compact lie groups. J Math Pures Appl (9). 2014;102(1):153–172.
   Web of Science ®Google Scholar
• Delgado J, Ruzhansky M, Tokmagambetov N. Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary. J Math Pures Appl (9). 2017;107(6):758–783.
   Web of Science ®Google Scholar
• Delgado J, Ruzhansky M. Schatten classes and traces on compact groups. Math Res Lett. 2017;24(4):979–1003.
   Web of Science ®Google Scholar
• Molahajloo S, Pirhayati M. Traces of pseudo-differential operators on compact and hausdorff groups. J Pseudo-Differ Oper Appl. 2013;4(3):361–369.
   Web of Science ®Google Scholar
• Dasgupta A, Wong MW. Hilbert–Schmidt and trace class pseudo-differential operators on the heisenberg group. J Pseudo-Differ Oper Appl. 2013;4:345–359.
   Web of Science ®Google Scholar
• Yin M, He J. H-Type group α-Weyl transform and pseudo-differential operators. Int J Math Anal. 2015;9(25):1201–1214.
   Google Scholar
• Dasgupta A, Nayek SK, Wong MW. Hilbert-Schmidt and trace class pseudo-differential operators and weyl transforms on the affine group. J. Pseudo-Differ. Oper. Appl. 2021;12(1):19 pp., Paper No. 11.
   PubMed Web of Science ®Google Scholar
• Kumar V, Mondal SS. Trace class and hilbert-Schmidt pseudo differential operators on step two nilpotent lie groups. Bull Sci Math. 2021;171:21 pp., Article ID 103015.
   Web of Science ®Google Scholar
• Ghosh S, Srivastava RK. Benedicks–Amrein–Berthier theorem for the Heisenberg motion group and quaternion Heisenberg group, (2019). arXiv:1904.04023.
   Google Scholar
• Ghosh S, Srivastava RK. Unbounded Weyl transforms on the Euclidean motion group and Heisenberg motion group, (2021). arXiv:2106.15704.
   Google Scholar
• Chattopadhyay A, Giri DK, Srivastava RK. Uniqueness of the Fourier transform on certain Lie groups, (2018). http://arxiv.org/abs/1607.03832v6.
   Google Scholar
• Ratnakumar PK, Rawat R, Thangavelu S. A restriction theorem for the heisenberg motion group. Studia Math. 1997;126:1–12.
   Web of Science ®Google Scholar
• Sen S. Segal-Bargmann transform and paley-Wiener theorems on heisenberg motion groups. Adv Pure Appl Math. 2016;7(1):13–28.
   Google Scholar
• Sugiura M. Unitary representations and harmonic analysis. Amsterdam, Tokyo: North-Holland Publishing Co., Kodansha, Ltd.; 1990. (North-Holland Math-ematical Library; 44).
   Google Scholar
• Thangavelu S. Harmonic analysis on the heisenberg group. Boston: Birkhäuser; 1998.
   Google Scholar
• Benson C, Jenkins J, Ratcliff G. Bounded K-spherical functions on heisenberg groups. J Funct Anal. 1992;105(2):409–443.
   Web of Science ®Google Scholar
• Wong MW. Weyl transforms. New York: Springer-Verlag; 1998.
   Google Scholar