Frontiers of Mathematics in China >

2010 , Vol. 5 >Issue 4: 777 - 792

DOI: https://doi.org/10.1007/s11464-010-0082-9

RESEARCH ARTICLE

Windowed-Kontorovich-Lebedev transforms

  • Jiman ZHAO , 1 ,
  • Lizhong PENG 2
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  • 1. School of Mathematical Sciences, Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing 100875, China
  • 2. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China

Received date: 08 Dec 2009

Accepted date: 05 Jun 2010

Published date: 05 Dec 2010

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

The aim of this paper is to study the boundedness of the windowed-Kontorovich-Lebedev transforms. For this purpose, we first define the translation associated to the Kontorovich-Lebedev transform and a generalized convolution product, then obtain some harmonic analysis results. We present a sufficient and necessary condition for the boundedness of the windowed-Kontorovich-Lebedev transform. Finally, we define the corresponding Weyl operator, and study the boundedness and compactedness of the Weyl operator with symbols in Lq (q ∈ [1, 2]) acting on Lp.

Key words： Kontorovich-Lebedev transform; translation; Weyl operator; Windowed-Kontorovich-Lebedev transform

Cite this article

Jiman ZHAO , Lizhong PENG . Windowed-Kontorovich-Lebedev transforms[J]. Frontiers of Mathematics in China, 2010 , 5(4) : 777 -792 . DOI: 10.1007/s11464-010-0082-9

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Bennett C, Sharpley R. Interpolation of Operators. New York: Academic Press, 1988

2
Bloom W R, Heyer H. Harmonic Analysis of Probability Measures on Hypergroups. de Gruyter Studies in Mathematics, Vol 20. Berlin: Walter de Gruyter Co, 1995

3
Boggiatto P, Buzano E, Rodino L. Global Hypoellipticity and Spectral Theory. Berlin: Akademie-Verlag, 1996

4
Boggiatto P, De Donno G, Oliaro A. Weyl quantization of Lebesgue spaces. Math Nachr, 2009, 282(12): 1656-1663

DOI

5
Boggiatto P, Rodino L. Quantization and pseudo-differential operators. Cubo Mat Educ, 2003, 5(1): 237-272

6
Bouattour L, Trimeche K. Beurling-Hörmander’s theorem for the Chébli-Trimèche transform. Glob J Pure Appl Math, 2005, 1(3): 342-357

7
Dachraoui A. Weyl-Bessel transforms. J Comput Appl Math, 2001, 133(1-2): 263-276

DOI

8
Gröchenig K H. Foundations of Time-Frequency Analysis. Boston: Birkhäuser, 2001

9
Lebedev N N. Special Functions and Their Applications. Moscow: Gosudarstv Izdat Tehn-Teor Lit, 1953

10
Oberhettinger F. Tables of Bessel Transforms. New York: Springer, 1972

11
Peng L Z, Zhao J M. Weyl transforms on the upper half plane. Rev Mat Complut, 2010, 23: 77-95

DOI

12
Rachdi L T, Trimèche K. Weyl transforms associated with the spherical mean operator. Anal Appl (Singap), 2003, 1(2): 141-164

DOI

13
Stein E M. Harmonic Analysis. Real-Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton: Princeton Univ Press, 1993

14
Terras A. Harmonic Analysis on Symmetric Space and Application, I. New York: Springer-Verlag, 1985

15
Toft J. Continuity properties for modulation spaces with applications to pseudodifferential calculus, I. J Funct Anal, 2004, 207(2): 399-429

DOI

16
Toft J. Continuity properties for modulation spaces with applications to pseudodifferential calculus, II. Ann Global Anal Geom, 2004, 26(1): 73-106

DOI

17
Watson G N. A Treatise on the Theory of Bessel Functions. 2nd ed. London: Cambridge Univ Press, 1966

18
Wong M W. Weyl Transform. New York: Springer-Verlag, 1998

19
Zhao J M, Peng L Z. Wavelet and Weyl transform associated with the spherical mean operator. Integral Equation and Operator Theory, 2004, 50: 279-290

DOI

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