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A unified approach for Littlewood-Paley decomposition of abstract Besov spaces


Author: Azita Mayeli
Journal: Proc. Amer. Math. Soc. 144 (2016), 1021-1028
MSC (2010): Primary 43X46; Secondary 41xxx
DOI: https://doi.org/10.1090/proc/12485
Published electronically: November 20, 2015
MathSciNet review: 3447656
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Abstract | References | Similar Articles | Additional Information

Abstract: We apply spectral theoretic methods to obtain a Littlewood-Paley decomposition of abstract inhomogeneous Besov spaces in terms of ``smooth'' and ``bandlimited'' functions. Well-known decompositions in several contexts are shown as special examples and are unified under the spectral theoretic approach.


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  • [1] M. Sh. Birman and M. Z. Solomjak, Spectral theory of selfadjoint operators in Hilbert space, Mathematics and its Applications (Soviet Series), D. Reidel Publishing Co., Dordrecht, 1987. Translated from the 1980 Russian original by S. Khrushchëv and V. Peller. MR 1192782 (93g:47001)
  • [2] Jens Gerlach Christensen and Gestur Ólafsson, Examples of coorbit spaces for dual pairs, Acta Appl. Math. 107 (2009), no. 1-3, 25-48. MR 2520008 (2010h:43002), https://doi.org/10.1007/s10440-008-9390-4
  • [3] Jens G. Christensen, Azita Mayeli, and Gestur Ólafsson, Coorbit description and atomic decomposition of Besov spaces, Numer. Funct. Anal. Optim. 33 (2012), no. 7-9, 847-871. MR 2966135, https://doi.org/10.1080/01630563.2012.682134
  • [4] Ronald A. DeVore and George G. Lorentz, Constructive approximation, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 303, Springer-Verlag, Berlin, 1993. MR 1261635 (95f:41001)
  • [5] Hans G. Feichtinger and K. H. Gröchenig, Banach spaces related to integrable group representations and their atomic decompositions. I, J. Funct. Anal. 86 (1989), no. 2, 307-340. MR 1021139 (91g:43011), https://doi.org/10.1016/0022-1236(89)90055-4
  • [6] Hartmut Führ, Paley-Wiener estimates for the Heisenberg group, Math. Nachr. 283 (2010), no. 2, 200-214. MR 2604118 (2011b:43014), https://doi.org/10.1002/mana.200810164
  • [7] Hartmut Führ and Azita Mayeli, Homogeneous Besov spaces on stratified Lie groups and their wavelet characterization, J. Funct. Spaces Appl. , posted on (2012), Art. ID 523586, 41. MR 2923803, https://doi.org/10.1155/2012/523586
  • [8] Michael Frazier and Björn Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), no. 4, 777-799. MR 808825 (87h:46083), https://doi.org/10.1512/iumj.1985.34.34041
  • [9] Daryl Geller and Azita Mayeli, Continuous wavelets and frames on stratified Lie groups. I, J. Fourier Anal. Appl. 12 (2006), no. 5, 543-579. MR 2267634 (2007g:42055), https://doi.org/10.1007/s00041-006-6002-4
  • [10] Daryl Geller and Azita Mayeli, Continuous wavelets on compact manifolds, Math. Z. 262 (2009), no. 4, 895-927. MR 2511756 (2010g:42089), https://doi.org/10.1007/s00209-008-0405-7
  • [11] Daryl Geller and Azita Mayeli, Nearly tight frames and space-frequency analysis on compact manifolds, Math. Z. 263 (2009), no. 2, 235-264. MR 2534117 (2011a:58050), https://doi.org/10.1007/s00209-008-0406-6
  • [12] Daryl Geller and Azita Mayeli, Besov spaces and frames on compact manifolds, Indiana Univ. Math. J. 58 (2009), no. 5, 2003-2042. MR 2583490 (2011d:42082), https://doi.org/10.1512/iumj.2009.58.3741
  • [13] Daryl Geller and Isaac Z. Pesenson, Band-limited localized Parseval frames and Besov spaces on compact homogeneous manifolds, J. Geom. Anal. 21 (2011), no. 2, 334-371. MR 2772076 (2012c:43013), https://doi.org/10.1007/s12220-010-9150-3
  • [14] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. MR 0089373 (19,664d)
  • [15] S. Krein, I. Pesenson, Interpolation Spaces and Approximation on Lie Groups, The Voronezh State University, Voronezh, 1990.
  • [16] S. G. Kreĭn, Yu. Ī. Petunīn, and E. M. Semënov, Interpolation of linear operators, Translations of Mathematical Monographs, vol. 54, American Mathematical Society, Providence, R.I., 1982. Translated from the Russian by J. Szűcs. MR 649411 (84j:46103)
  • [17] J.-L. Lions, Théorèmes de trace et d'interpolation. I, Ann. Scuola Norm. Sup. Pisa (3) 13 (1959), 389-403. MR 0119092 (22 #9858)
  • [18] Jaak Peetre, New thoughts on Besov spaces, Mathematics Department, Duke University, Durham, N.C., 1976. Duke University Mathematics Series, No. 1. MR 0461123 (57 #1108)

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Additional Information

Azita Mayeli
Affiliation: Department of Mathematics and Computer Sciences, City University of New York, Queensborough, Bayside, 222-05 56th Avenue, New York, New York 11364
Email: amayeli@qcc.cuny.edu

DOI: https://doi.org/10.1090/proc/12485
Keywords: Inhomogeneous Besov space, Paley-Wiener space, Littlewood-Paley decomposition
Received by editor(s): February 7, 2014
Published electronically: November 20, 2015
Additional Notes: The research was supported by The Professional Staff Congress-City University of New York Grant.
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2015 American Mathematical Society

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