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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 1, Pages 87–91 (Mi faa3101)  

This article is cited in 17 scientific papers (total in 17 papers)

Brief communications

On Multipliers on Compact Lie Groups

M. V. Ruzhanskya, J. Wirthb

a Imperial College London, Department of Mathematics
b University of Stuttgart

Abstract: In this note we announce $L^p$ multiplier theorems for invariant and noninvariant operators on compact Lie groups in the spirit of the well-known Hörmander–Mikhlin theorem on $\mathbb R^n$ and its versions on the torus $\mathbb T^n$. Applications to mapping properties of pseudo-differential operators on $L^p$-spaces and to a priori estimates for nonhypoelliptic operators are given.

Keywords: multiplier, pseudo-differential operator, Lie group


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English version:
Functional Analysis and Its Applications, 2013, 47:1, 72–75

Bibliographic databases:

UDC: 517.518.12
Received: 18.07.2011

Citation: M. V. Ruzhansky, J. Wirth, “On Multipliers on Compact Lie Groups”, Funktsional. Anal. i Prilozhen., 47:1 (2013), 87–91; Funct. Anal. Appl., 47:1 (2013), 72–75

Citation in format AMSBIB
\by M.~V.~Ruzhansky, J.~Wirth
\paper On Multipliers on Compact Lie Groups
\jour Funktsional. Anal. i Prilozhen.
\yr 2013
\vol 47
\issue 1
\pages 87--91
\jour Funct. Anal. Appl.
\yr 2013
\vol 47
\issue 1
\pages 72--75

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    This publication is cited in the following articles:
    1. J. Delgado, M. Ruzhansky, “$L^p$-nuclearity, traces, and Grothendieck-Lidskii formula on compact Lie groups”, J. Math. Pures Appl. (9), 102:1 (2014), 153–172  crossref  mathscinet  zmath  isi  scopus
    2. M. Ruzhansky, J. Wirth, “Global functional calculus for operators on compact Lie groups”, J. Funct. Anal., 267:1 (2014), 144–172  crossref  mathscinet  zmath  isi  scopus
    3. M. Ruzhansky, V. Turunen, J. Wirth, “Hörmander class of pseudo-differential operators on compact Lie groups and global hypoellipticity”, J. Fourier Anal. Appl., 20:3 (2014), 476–499  crossref  mathscinet  zmath  isi  scopus
    4. B. Kanguzhin, N. Tokmagambetov, K. Tulenov, “Pseudo-differential operators generated by a non-local boundary value problem”, Complex Var. Elliptic Equ., 60:1 (2015), 107–117  crossref  mathscinet  zmath  isi  scopus
    5. M. Ruzhansky, J. Wirth, “$L^p$ Fourier multipliers on compact Lie groups”, Math. Z., 280:3-4 (2015), 621–642  crossref  mathscinet  zmath  isi  scopus
    6. R. H. Akilzhanoff, E. D. Nursultanov, M. V. Ruzhanskii, “Hardy–Littlewood–Paley-type Inequalities on Compact Lie Groups”, Math. Notes, 100:2 (2016), 309–312  mathnet  crossref  crossref  mathscinet  isi  elib
    7. R. Akylzhanov, E. Nursultanov, M. Ruzhansky, “Hardy–Littlewood–Paley inequalities and Fourier multipliers on SU(2)”, Studia Math., 234:1 (2016), 1–29  crossref  mathscinet  zmath  isi  elib  scopus
    8. M. B. Ghaemi, M. J. Birgani, “$L^p$-boundedness, compactness of pseudo-differential operators on compact Lie groups”, J. Pseudo-Differ. Oper. Appl., 8:1 (2017), 1–11  crossref  mathscinet  zmath  isi  scopus
    9. C. Baccar, N. Ben Hamadi, S. Omri, “Fourier multipliers associated with singular partial differential operators”, Oper. Matrices, 11:1 (2017), 37–53  crossref  mathscinet  zmath  isi  scopus
    10. J. Delgado, M. Ruzhansky, “Schatten classes and traces on compact groups”, Math. Res. Lett., 24:4 (2017), 979–1003  crossref  mathscinet  zmath  isi
    11. D. Cardona, “Besov continuity of pseudo-differential operators on compact Lie groups revisited”, C. R. Math. Acad. Sci. Paris, 355:5 (2017), 533–537  crossref  mathscinet  zmath  isi  scopus
    12. D. Cardona, “Besov continuity for global operators on compact Lie groups: the critical case $p=q=\infty$”, Trans. A Razmadze Math. Inst., 172:3, A (2018), 354–360  crossref  mathscinet  isi
    13. Daher R., Delgado J., Ruzhansky M., “Titchmarsh Theorems For Fourier Transforms of Holder-Lipschitz Functions on Compact Homogeneous Manifolds”, Mon.heft. Math., 189:1 (2019), 23–49  crossref  isi
    14. Akylzhanov R. Ruzhansky M. Nursultanov E., “Hardy-Littlewood, Hausdorff-Young-Paley Inequalities, and l-P- l-Q Fourier Multipliers on Compact Homogeneous Manifolds”, J. Math. Anal. Appl., 479:2 (2019), 1519–1548  crossref  mathscinet  zmath  isi
    15. Delgado J., Ruzhansky M., “L-P-Bounds For Pseudo-Differential Operators on Compact Lie Groups”, J. Inst. Math. Jussieu, 18:3 (2019), 531–559  crossref  mathscinet  zmath  isi
    16. Akylzhanov R. Ruzhansky M., “L-P-l-Q Multipliers on Locally Compact Groups”, J. Funct. Anal., 278:3 (2020), UNSP 108324  crossref  mathscinet  isi
    17. Kirilov A., de Moraes W.A.A., Ruzhansky M., “Global Hypoellipticity and Global Solvability For Vector Fields on Compact Lie Groups”, J. Funct. Anal., 280:2 (2021), 108806  crossref  mathscinet  zmath  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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