Decomposition of Besov and Triebel-Lizorkin spaces on the sphere

Journal of Functional Analysis

Volumn 238, Issue 2, 2006, Pages 530-564

  Narcowich, F ^a   Petrushev, P ^b   Ward, J ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

^b UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

Besov space; Frame; Littlewood Paley theory; m Term approximation; Spherical harmonics; Triebel Lizorkin space

Indexed keywords

EID: 33746265509     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2006.02.011     Document Type: Article

References (20)

1. Brown G., and Dai F. Approximation of smooth functions on compact two-point homogeneous spaces. J. Funct. Anal. 220 (2005) 401-423
2. L. Colzani, Hardy and Lipschitz spaces on unit spheres, PhD thesis, Washington University, St. Louis, 1982
3. Dai F. Characterization of function spaces on the sphere using frames. math.CA/0510084
4. Frazier M., and Jawerth B. Decomposition of Besov spaces. Indiana Univ. Math. J. 34 (1985) 777-799
5. Frazier M., and Jawerth B. A discrete transform and decomposition of distribution spaces. J. Funct. Anal. 93 (1990) 34-170
6. Frazier M., Jawerth B., and Weiss G. Littlewood-Paley Theory and the Study of Function Spaces. CBMS Reg. Conf. Ser. Math. vol. 79 (1991), Amer. Math. Soc., Providence, RI
7. Hörmander L. The spectral function of an elliptic operator. Acta Math. 121 (1968) 193-218
8. Meyers Y. Ondelletes et Opérateurs I: Ondelletes (1990), Hermann, Paris
9. Mhaskar H., Narcowich F., and Ward J. Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature. Math. Comp. 70 (2001) 1113-1130
10. Müller C. Spherical Harmonics. Lecture Notes in Math. vol. 17 (1966), Springer-Verlag, Berlin
11. F. Narcowich, P. Petrushev, J. Ward, Localized tight frames on spheres, SIAM J. Math. Analysis, in press
12. Peetre J. New Thoughts on Besov Spaces. Duke Univ. Math. Ser. (1976), Duke Univ. Press, Durham, NC
13. Petrushev P., and Popov V. Rational Approximation of Real Functions (1987), Cambridge Univ. Press, Cambridge
14. Petrushev P., and Xu Y. Localized polynomial frames on the interval with Jacobi weights. J. Fourier Anal. Appl. 11 (2005) 557-575
15. Stein E. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals (1993), Princeton Univ. Press, Princeton, NJ
16. Stein E., and Weiss G. Fourier Analysis on Euclidean Spaces (1971), Princeton Univ. Press, Princeton, NJ
17. Strichartz R. Multipliers for spherical harmonics. Trans. Amer. Math. Soc. 169 (1972) 115-124
18. Szegö G. Orthogonal Polynomials. Amer. Math. Soc. Colloq. Publ. vol. 23 (1975), Amer. Math. Soc., Providence, RI
19. Triebel H. Theory of Function Spaces. Monogr. Math. vol. 78 (1983), Birkhäuser, Basel
20. Triebel H. Theory of Function Spaces II. Monogr. Math. vol. 84 (1992), Birkhäuser, Basel