Multivariate polynomial inequalities with respect to doubling weights and A∞ weights

Journal of Functional Analysis

Volumn 235, Issue 1, 2006, Pages 137-170

  Dai, Feng ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

A weights; Doubling weights; Multivariate polynomial inequalities; Positive cubature formulae; Spherical harmonics

Indexed keywords

EID: 33645945289     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2005.09.009     Document Type: Article

References (27)

1. Bonami A., and Clerc J.L. Sommes de Cesàro et multiplicateurs des dèveloppments en harmonique sphériques. Trans. Amer. Math. Soc. 183 (1973) 223-263
2. Borwein P., and Erdélyi T. Polynomials and Polynomial Inequalities. Grad. Texts in Math. vol. 161 (1995), Springer-Verlag, New York
3. Brown G., and Dai F. Approximation of smooth functions on compact two-point homogeneous spaces. J. Funct. Anal. 220 (2005) 401-423
4. Ditzian Z. Jackson-type inequality on the sphere. Acta Math. Hungar. 102 1-2 (2004) 1-35
5. Dunkl C.F., and Xu Y. Orthogonal Polynomials of Several Variables. Encyclopedia Math. Appl. vol. 81 (2001), Cambridge Univ. Press, Cambridge
6. Erdélyi T. Remez-type inequalities on the size of generalized polynomials. J. London Math. Soc. (2) 45 2 (1992) 255-264
7. Erdélyi T. Remez-type inequalities and their applications. J. Comput. Appl. Math. 47 2 (1993) 167-209
8. Erdélyi T. Notes on inequalities with doubling weights. J. Approx. Theory 100 1 (1999) 60-72
9. Erdélyi T. Markov-Bernstein-type inequality for trigonometric polynomials with respect to doubling weights on [ - ω, ω ]. Constr. Approx. 19 3 (2003) 329-338
10. Helgason S. Groups and Geometric Analysis: Integral Geometry, Invariant Differential Operators, and Spherical Functions (2000), Amer. Math. Soc., Providence, RI
11. Li Z., and Xu Y. Summability of orthogonal expansions of several variables. J. Approx. Theory 122 2 (2003) 267-333
12. Mastroianni G., and Totik V. Jackson type inequalities for doubling weights II. East J. Approx. 5 1 (1999) 101-116
13. ∞ weights. Constr. Approx. 16 1 (2000) 37-71
14. Mastroianni G., and Totik V. Best approximation and moduli of smoothness for doubling weights. J. Approx. Theory 110 2 (2001) 180-199
15. Mhaskar H.N., Narcowich F.J., and Ward J.D. Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature. Math. Comp. 70 (2001) 1113-1130 Corrigendum
16. Mhaskar H.N., Narcowich F.J., and Ward J.D. Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature. Math. Comp. 71 (2001) 453-454
17. Müller C. Spherical Harmonics. Lecture Notes in Math. vol. 17 (1966), Springer-Verlag, Berlin
18. Narcowich F.J., Petrushev P., and Ward J.D. Localized tight frames on spheres. preprint (2004). http://www.math.sc.edu~pencho/
19. Petrova G. Cubature formulae for spheres, simplices and balls. J. Comput. Appl. Math. 162 2 (2004) 483-496
20. Szegö G. Orthogonal Polynomials (1967), Amer. Math. Soc., New York
21. Torchinsky A. Real-Variable Methods in Harmonic Analysis. Pure Appl. Math. vol. 123 (1986), Academic Press, Orlando, FL
22. Wang K., and Li L. Harmonic Analysis and Approximation on the Unit Sphere (2000), Science Press, Beijing
23. Xu Y. Orthogonal polynomials and cubature formulae on spheres and on balls. SIAM J. Math. Anal. 29 3 (1998) 779-793
24. Xu Y. Orthogonal polynomials and summability in Fourier orthogonal series on spheres and on balls. Math. Proc. Cambridge Philos. Soc. 131 1 (2001) 139-155
25. Xu Y. Orthogonal polynomials and cubature formulae on balls, simplices, and spheres. J. Comput. Appl. Math. 127 1-2 (2001) 349-368
26. Xu Y. Weighted approximation of functions on the unit sphere. Constr. Approx. 21 1 (2004) 1-28
27. Xu Y. Almost everywhere convergence of orthogonal expansions of several variables. Constr. Approx. 22 1 (2005) 67-93