Extrapolation from A∞ weights and applications

Journal of Functional Analysis

Volumn 213, Issue 2, 2004, Pages 412-439

  Cruz Uribe, David ^a   Martell, J M ^b   Pérez, Carlos ^c  

^a TRINITY COLLEGE   (United States)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^c UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Commutators; Extrapolation; Good inequalities; Maximal operators; Muckenhoupt weights; Potential operators; Singular integrals

Indexed keywords

EID: 3242876510     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2003.09.002     Document Type: Article

References (40)

1. Adams D.R. A note on Riesz potentials Duke Math. J. 42 1975 765-778
2. ∞ weights for various singular integral operators Boll. Un. Mat. Ital. A 8 7 1994 123-133
3. Anderson K.F. John R.T. Weighted inequalities for vector-valued maximal functions and singular integrals Stud. Math. 69 1980 19-31
4. Benedek A. Calderón A.P. Panzone R. Convolution operators on Banach space valued functions Proc. Natl. Acad. Sci. USA 48 1962 356-365
5. Bennett C. Sharpley R.C. Interpolation of Operators Pure and Applied Mathematics Vol. 129 1988 Academic Press New York
6. Burkholder D.L. Gundy R.F. Extrapolation and interpolation of quasilinear operators on martingales Acta Math. 124 1970 249-304
7. Chang S.-Y.A. Wilson J.M. Wolff T.H. Some weighted norm inequalities concerning the Schrodinger operators Comment. Math. Helv. 60 1985 217-246
8. Chanillo S. A note on commutators Indiana Univ. Math. J. 31 1982 7-16
9. Coifman R. Distribution function inequalities for singular integrals Proc. Natl. Acad. Sci. USA 69 1972 2838-2839
10. Coifman R. Fefferman C. Weighted norm inequalities for maximal functions and singular integrals Stud. Math. 51 1974 241-250
11. Cruz-Uribe D. A. Fiorenza SFO, Endpoint estimates and weighted norm inequalities for commutators of fractional integrals Publ. Mat. 47 2003 103-131
12. Duoandikoetxea J. Fourier Analysis Graduate Studies in Mathematics Vol. 29 2000 American Mathematical Society Providence, RI
13. Fefferman C. Stein E.M. Some maximal inequalities Amer. J. Math. 93 1971 107-115
14. p spaces in several variables Acta Math. 129 1972 137-193
15. p-weights Proc. Amer. Math. Soc. 87 1983 422-426
16. García-Cuerva J. Rubio de Francia J.L. Weighted Norm Inequalities and Related Topics North-Holland Mathematical Studies Vol. 116 1985 North-Holland Amsterdam
17. L. Grafakos, J.M. Martell, Extrapolation of weighted norm inequalities for multivariable operators and applications, J. Geom. Anal., to appear
18. Grafakos L. Torres R. Multilinear Calderón-Zygmund theory Adv. Math. 165 2002 124-164
19. Grafakos L. Torres R. Maximal operator and weighted norm inequalities for multilinear singular integrals Indiana Univ. Math. J. 51 5 2002 1261-1276
20. Gundy R.F. Wheeden R.L. Weighted integral inequalities for the nontangential maximal function, Lusin area integral, and Walsh-Paley series Stud. Math. 49 1973 101-118
21. Jawerth B. Weighted inequalities for maximal operators: linearization, localization and factorization Amer. J. Math. 108 1986 361-414
22. Kerman R. Sawyer E. The trace inequality and eigenvalue estimates for Schrödinger operators Ann. Inst. Fourier 36 1986 207-228
23. A.K. Lerner, Weighted norm inequalities for the local sharp maximal function, J. Fourier Anal. Appl., to appear
24. J.M. Martell, Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications, Stud. Math., to appear
25. J.M. Martell, C. Pérez, R. Trujillo-González, Lack of natural weighted estimates for some singular integral operators, Trans. Amer. Math. Soc., to appear.
26. Muckenhoupt B. Wheeden R. Weighted norm inequalities for fractional integrals Trans. Amer. Math. Soc. 192 1974 261-274
27. Pérez C. Weighted norm inequalities for general maximal operators Publ. Mat. 35 1991 169-186
28. Pérez C. Two weighted inequalities for potential and fractional type maximal operators Indiana Univ. Math. J. 43 1994 663-683
29. p-weighted Sobolev inequalities Ann. Inst. Fourier 45 3 1995 1-16
30. Pérez C. Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function J. Fourier Anal. Appl. 3 1997 743-756
31. C. Pérez, R. Torres, Sharp maximal function estimates for multilinear singular integrals, Harmonic Analysis at Mount Holyoke (South Hadley, MA, 2001), Contemp. Math., Vol. 320, Amer. Math. Soc., Providence, RI, 2003, pp. 323-331
32. Pérez C. Wheeden R.L. Uncertainty principle estimates for vector fields J. Funct. Anal. 181 2001 146-188
33. Rao M. Ren Z. Theory of Orlicz spaces Pure and Applied Mathematics Vol. 146 1991 Marcel Dekker New York
34. p weights Amer. J. Math. 106 1984 533-547
35. Rubio de Francia J.L. Ruiz F.J. Torrea J.L. Calderón-Zygmund theory for operator-valued kernels Adv. Math. 62 1986 7-48
36. Sawyer E.T. Wheeden R.L. Weighted inequalities for fractional integrals on euclidean and homogeneous spaces Amer. J. Math. 114 1992 813-874
37. Segovia C. Torrea J.L. Weighted inequalities for commutators of fractional and singular integrals Publ. Mat. 35 1991 209-235
38. Torchinsky A. Real-Variable Methods in Harmonic Analysis 1986 Academic Press New York
39. Wilson J.M. A sharp inequality for the square function Duke Math. J. 55 1987 879-887
40. L. Yan, On commutators of fractional integrals, preprint 2002