M. Ruzhansky, V. Turunen, Pseudo-Differential Operators and Symmetries, Birkhäuser, 2010. 724pp.
Link to publisher, Description and Samples, BookmetrixZB ReviewMR Review

In this book the global analysis of pseudo-differential operators is consistently developed in the setting of compact Lie groups. The book also contains the background material on related topics of analysis, and is related to time-frequency analysis. Some extracts from the book can be downloaded here.

Book-Fischer-Ruzhansky-cover-1V. Fischer, M. Ruzhansky, Quantization on Nilpotent Lie Groups, Progress in Math., Vol. 314, Birkhäuser, 2016. 557pp. BookmetrixZB Review, MR review

In this book the global quantization constructions of the previous work have been developed in the setting of general graded Lie groups. There is also an extensive presentation of the background analysis on stratified, graded, and general homogeneous groups. This book is open access and can be downloaded here.

cover-ruzhansky-suragan-hardyM. Ruzhansky, D. Suragan, Hardy inequalities on homogeneous groups (100 Years of Hardy Inequalities), Progress in Math., Vol. 327, Birkhäuser, 2019.573 pp. 

This book is the winner of the Ferran Sunyer i Balaguer Prize 2018

This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein’s homogeneous (Lie) groups.

⛹ Publications of Michael Ruzhansky can be found and downloaded here.

on stratified groups: 

  1. Ruzhansky M., Suragan D., On Kac principle of not feeling the boundary for the Kohn Laplacian on the Heisenberg group, Proc. Amer. Math. Soc., 144 (2016), 709-721. arxivlink
  2. Ruzhansky M., Yessirkegenov N., Rellich inequalities for sub-Laplacians with driftarxiv
  3. Ruzhansky M., Yessirkegenov N., Factorizations and Hardy-Rellich inequalities on stratified groupsarxiv
  4. Ruzhansky M., Sabitbek B., Suragan D., Weighted Lp-Hardy and Lp-Rellich inequalities with boundary terms on stratified Lie groupsarxiv
  5. Ruzhansky M., Suragan D., Green’s identities, comparison principle and uniqueness of positive solutions for nonlinear p-sub-Laplacian equations on stratified Lie groupsarxiv
  6. Ruzhansky M., Suragan D., Elements of potential theory on Carnot groups, Funct. Anal. Appl., to appear.
  7. Ruzhansky M., Suragan D., Yessirkegenov N., Caffarelli-Kohn-Nirenberg and Sobolev type inequalities on stratified Lie groups, NoDEA Nonlinear Differential Equations Appl, 24 (2017), no. 5, 24:56. offprint (open access)arxivlink
  8. Garofalo N., Ruzhansky M., Suragan D., On Green functions for Dirichlet sub-Laplacians on H-type groups, J. Math. Anal. Appl., 452 (2017), 896-905. offprint (open access)linkarxiv
  9. Ruzhansky M., Suragan D., Layer potentials, Green formulae, Kac problem, and refined Hardy inequality on homogeneous Carnot groups, Adv. Math., 308 (2017), 483-528. offprint (open access)arxivlink
  10. Ruzhansky M., Suragan D., On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and p-sub-Laplacian inequalities on stratified groups, J. Differential Equations, 262 (2017), 1799-1821. offprint (open access)arxivlink

on graded groups: 

  1. Ruzhansky M., Yessirkegenov N., Critical Sobolev, Gagliardo-Nirenberg, Trudinger and Brezis-Gallouet-Wainger inequalities, best constants, and ground states on graded groupsarxiv
  2. Ruzhansky M., Taranto C., Time-dependent wave equations on graded groupsarxiv
  3. Ruzhansky M., Tokmagambetov N., Yessirkegenov N., Best constants in Sobolev and Gagliardo-Nirenberg inequalities on graded groups and ground states for higher order nonlinear subelliptic equationsarxiv
  4. Ruzhansky M., Tokmagambetov N., Nonlinear damped wave equations for the sub-Laplacian on the Heisenberg group and for Rockland operators on graded Lie groupsarxiv
  5. Cardona D., Ruzhansky M., Littlewood-Paley theorem, Nikolskii inequality, Besov spaces, Fourier and spectral multipliers on graded Lie groupsarxiv
  6. Fischer V., Ruzhansky M., Fourier multipliers on graded Lie groupsarxiv
  7. Fischer V., Ruzhansky M., Sobolev spaces on graded groups, Ann. Inst. Fourier, 67 (2017), 1671-1723. offprint (open access)arxivlink
  8. Cardona D., Ruzhansky M., Multipliers for Besov spaces on graded Lie groups, C. R. Acad. Sci. Paris355 (2017), 400-405. offprint (open access)link
  9. Fischer V., Ruzhansky M., A pseudo-differential calculus on graded nilpotent Lie groups, in Fourier Analysis, pp. 107-132, Trends in Mathematics, Birkhauser, 2014. arxivlink
  10. Fischer V., Ruzhansky M., Lower bounds for operators on graded Lie groups, C. R. Acad. Sci. Paris, Ser I, 351 (2013), 13-18. arxivlink

on general homogeneous groups: 

  1. Ruzhansky M., Suragan D., A note on stability of Hardy inequalitiesAnn. Funct. Anal., to appear, arxiv
  2. Ruzhansky M., Suragan D., Yessirkegenov N., Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability and superweights for Lp-weighted Hardy inequalities, Trans. Amer. Math. Soc., to appear, arxiv
  3. Ruzhansky M., Suragan D., Yessirkegenov N., Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spacesarxiv
  4. Ruzhansky M., Suragan D., Yessirkegenov N., Sobolev inequalities, Euler-Hilbert-Sobolev and Sobolev-Lorentz-Zygmund spaces on homogeneous groupsarxiv
  5. Ozawa T., Ruzhansky M., Suragan D., Lp-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groupsarxiv
  6. Ruzhansky M., Suragan D., Critical Hardy inequalitiesarxiv
  7. Ruzhansky M., Suragan D., Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups, Adv. Math., 317 (2017), 799-822. offprint (open access)arxivlink
  8. Ruzhansky M., Suragan D., Anisotropic L2-weighted Hardy and L2-Caffarelli-Kohn-Nirenberg inequalities, Commun. Contemp. Math., 19 (2017), no. 6, 1750014, 12pp. offprint (open access)arxivlink
  9. Ruzhansky M., Suragan D., Yessirkegenov N., Extended Caffarelli-Kohn-Nirenberg inequalities and superweights for Lp-weighted Hardy inequalities, C. R. Acad. Sci. Paris355 (2017), 694-698. offprint (open access)link
  10. Ruzhansky M., Suragan D., Uncertainty relations on nilpotent Lie groups, Proc. R. Soc. A, 473 (2017), no. 2201, 20170082, 12pp. offprint (open access)arxivlink

on compact Lie groups:

  1. Cardona D., Ruzhansky M., Boundedness of pseudo-differential operators in subelliptic Sobolev and Besov spaces on compact Lie groups. arxiv
  2. Akylzhanov R., Liflyand E., Ruzhansky M., Re-expansions on compact Lie groups. arxiv