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    Abdelmoula, F. Baklouti, A. and Lahyani, D. 2013. An L p -L q analog of miyachi’s theorem for nilpotent lie groups and sharpness problems. Mathematical Notes, Vol. 94, Issue. 1-2, p. 3.


    Абдельмула, Abdelmoula, Баклути, Baklouti, Лахьяни, and Lahyani, 2013. $L^p$ - $L^q$ аналог теоремы Миячи для нильпотентных групп Ли и проблема точности. Математические заметки, Vol. 94, Issue. 1, p. 3.


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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 88, Issue 1
  • February 2010, pp. 1-17

VARIANTS OF MIYACHI’S THEOREM FOR NILPOTENT LIE GROUPS

  • ALI BAKLOUTI (a1) and SUNDARAM THANGAVELU (a2)
  • DOI: http://dx.doi.org/10.1017/S144678870900038X
  • Published online: 01 January 2010
Abstract
Abstract

We formulate and prove two versions of Miyachi’s theorem for connected, simply connected nilpotent Lie groups. This allows us to prove the sharpness of the constant 1/4 in the theorems of Hardy and of Cowling and Price for any nilpotent Lie group. These theorems are proved using a variant of Miyachi’s theorem for the group Fourier transform.

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Copyright
Corresponding author
For correspondence; e-mail: veluma@math.iisc.ernet.in
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The first author was supported by D.G.R.S.R.T., Research Unity 00 UR 1501 and the second author by a J.C. Bose Fellowship from DST.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]A. Baklouti and E. Kaniuth , ‘On Hardy’s uncertainty principle for connected nilpotent Lie groups’, Math. Z. 259(2) (2008), 233247.

[3]A. Baklouti and N. Ben Salah , ‘The Lp-Lq version of Hardy’s theorem on nilpotent Lie groups’, Forum Math. 18(2) (2006), 245262.

[4]A. Baklouti and N. Ben Salah , ‘On theorems of Beurling and Cowling–Price for certain nilpotent Lie groups’, Bull. Sci. Math. 132(6) (2008), 529550.

[5]A. Baklouti , K. Smaoui and J. Ludwig , ‘Estimate of Lp-Fourier transform norm on nilpotent Lie groups’, J. Funct. Anal. 199 (2003), 508520.

[6]M. Cowling and J. Price , ‘Generalizations of Heisenberg’s inequality’, in: Harmonic Analysis, Lecture Notes in Mathematics, 992 (eds. G. Mauceri , F. Ricci and G. Weiss ) (Springer, Berlin, 1983).

[7]G. Folland and A. Sitaram , ‘The uncertainty principle: a mathematical survey’, J. Fourier Anal. Appl. 3(3) (1997), 207238.

[12]S. Thangavelu , ‘Hardy’s theorem on the Heisenberg group revisited’, Math. Z. 242 (2002), 761779.

[13]S. Thangavelu , An Introduction to the Uncertainty Principle: Hardy’s Theorem on Lie Groups, Progress in Mathematics, 217 (Birkhäuser, Boston, MA, 2004).

[14]S. Thangavelu , ‘A survey of Hardy type theorems’, in: Advances in Analysis, (eds. H. G. W. Begehr , R. P. Gilbert , M. E. Muldoon and M. W. Wong ) (World Scientific, Singapore, 2005), pp. 3970.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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