On the two-weight problem for singular integral operators

 Access to full text

 Full (PDF)

1. [1] D. Cruz-Uribe, SFO – A. Fiorenza, The $A_{\infty }$ property for Young functions and weighted norm inequalities, Houston J. Math., to appear. Zbl1041.42009MR1876947
2. [2] D. Cruz-Uribe, SFO – C. Pérez, Sharp two-weight, weak-type norm inequalities for singular integral operators, Math. Res. Let. 6 (1999), 417-428. Zbl0961.42013MR1713140
3. [3] D. Cruz-Uribe, SFO – C. Pérez, Two-weight, weak-type norm inequalities for fractional integrals, Calderón-Zygmund operators and commutators, Indiana Math. J. 49 (2000), 697-721. Zbl1033.42009MR1793688
4. [4] Duoandikoetxea, J., “Fourier Analysis”, Grad. Studies Math. 29, Amer. Math. Soc., Providence, 2000. Zbl0969.42001MR1800316
5. [5] C. Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9-36. Zbl0188.42601MR257819
6. [6] N. Fujii, A condition for a two-weight norm inequality for singular integral operators, Studia Math. 98 (1991), 175-190. Zbl0732.42012MR1115188
7. [7] J. García-Cuerva – E. Harboure – C. Segovia – J. L. Torrea, Weighted norm inequalities for commutators of strongly singular integrals, Indiana Univ. Math. J. 40 (1991), 1398-1420. Zbl0765.42012MR1142721
8. [8] J. García-Cuerva – J. L. Rubio de Francia, “Weighted Norm Inequalities and Related Topics”, North Holland Math. Studies 116, North Holland, Amsterdam, 1985. Zbl0578.46046MR848136
9. [9] L. Hörmander, Pseudo-differential operators and hypoelliptic equations, Proc. Symp. Pure Math. 10 (1967), 138-183. Zbl0167.09603MR383152
10. [10] S. Janson, Mean oscillation and commutators of singular integrals, Ark. Mat. 16 (1978), 263-270. Zbl0404.42013MR524754
11. [11] J.-L. Journé, “Zygmund Operators, Pseudo-Differential Operators and the Cauchy Integral of Calderón”, Lecture Notes in Mathematics, 994, Springer Verlag, Berlin, 1983. Zbl0508.42021
12. [12] N. H. Katz – C. Pereyra, On the two weights problem for the Hilbert transform, Rev. Mat. Iberoamericana 13 (1997), 189-210. Zbl0908.49029MR1462332
13. [13] M. A. Leckband, Structure results on the maximal Hilbert transform and two-weight norm inequalities, Indiana Math. J. 34 (1985), 259-275. Zbl0586.42010MR783915
14. [14] B. Muckenhoupt, Weighted norm inequalities for the Hardy-Littlewood maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. Zbl0236.26016MR293384
15. [15] B. Muckenhoupt – R. L. Wheeden, Norm inequalities for Littlewood-Paley function $g_{\lambda }^{*}$, Trans. Amer. Math. Soc. 191 (1974), 95-111. Zbl0289.44005MR387973
16. [16] B. Muckenhoupt – R. Wheeden, Two weight function norm inequalities for the Hardy-Littlewood maximal function and the Hilbert transform, Studia Math. 60 (1976), 279-294. Zbl0336.44006MR417671
17. [17] C. J. Neugebauer, Inserting $A_p$-weights, Proc. Amer. Math. Soc. 87 (1983), 644-648. Zbl0521.42019MR687633
18. [18] R. O’Neil, Fractional integration in Orlicz spaces, Trans. Amer. Math. Soc. 115 (1965), 300-328. Zbl0132.09201MR194881
19. [19] C. Pérez, Two weighted inequalities for potential and fractional type maximal operators, Indiana Math. J. 43 (1994), 663-683. Zbl0809.42007MR1291534
20. [20] C. Pérez, On sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator between weighted $L^p$-spaces with different weights, Proc. London Math. Soc. 71 (1995), 135-57. Zbl0829.42019MR1327936
21. [21] C. Pérez, Endpoint estimates for commutators of singular integral operators, J. Func. Anal. 128 (1995), 163-185. Zbl0831.42010MR1317714
22. [22] C. Pérez, Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function, J. Fourier Anal. Appl. 3 (6) (1997), 743-756. Zbl0894.42006MR1481632
23. [23] C. Pérez – G. Pradolini, Sharp weighted endpoint estimates for commutators of singular integral operators, Michigan Math. J. 49 (2001), 23-37. Zbl1010.42007MR1827073
24. [24] C. Pérez – R. Wheeden, Uncertainty principle estimates for vector fields, J. Func. Anal. 181 (2001), 146-188. Zbl0982.42010MR1818113
25. [25] D. H. Phong – E. M. Stein, Hilbert integrals, singular integrals and Radon transforms, Acta Math. 157 (1985), 99-157. Zbl0622.42011MR857680
26. [26] M. M. Rao – Z. D. Ren, “Theory of Orlicz Spaces”, Marcel Dekker, New York, 1991. Zbl0724.46032MR1113700
27. [27] Y. Rakotondratsimba, Two weight norm inequality for Calderón-Zygmund operators, Acta Math. Hungar. 80 (1998), 39-54. Zbl0914.47007MR1624522
28. [28] Y. Rakotondratsimba, Two-weight inequality for commutators of singular integral operators, Kobe J. Math. 16 (1999), 1-20. Zbl0940.42011MR1723543
29. [29] J. L. Rubio de Francia – F. J. Ruiz – J. L. Torrea, Calderón-Zygmund theory for operator-valued kernels, Adv. in Math. 62, (1986), 7-48. Zbl0627.42008MR859252
30. [30] E. T. Sawyer, A characterization of a two weight norm weight inequality for maximal operators, Studia Math. 75 (1982), 1-11. Zbl0508.42023MR676801
31. [31] C. Segovia – J. L. Torrea, Higher order commutators for vector-valued Calderón-Zygmund operators, Trans. Amer. Math. Soc. 336 (1993), 537-556. Zbl0799.42009MR1074151
32. [32] E. M. Stein, Note on the class L logL, Studia Math. 32 (1969), 305-310. Zbl0182.47803MR247534
33. [33] E. M. Stein, “Singular Integrals and Differentiability Properties of Functions”, Princeton University Press, Princeton, 1970. Zbl0207.13501MR290095
34. [34] J.-O. Strömberg – A. Torchinsky, “Weighted Hardy Spaces”, Lecture Notes in Mathematics, 1381, Springer Verlag, Berlin, 1989. Zbl0676.42021MR1011673
35. [35] A. Torchinsky, “Real-Variable Methods in Harmonic Analysis”, Academic Press, New York, 1986. Zbl0621.42001MR869816
36. [36] S. Treil – A. Volberg – D. Zheng, Hilbert Transform, Toeplitz operators and Hankel operators, and invariant $A_{\infty }$ weights, Rev. Mat. Iberoamericana 13 (1997), 319-360. Zbl0896.42009MR1617653
37. [37] G. Weiss, A note on Orlicz spaces, Portugal. Math. 15 (1950), 35-47. Zbl0071.33001MR82645
38. [38] J. M. Wilson, Weighted norm inequalities for the continuous square functions, Trans. Amer. Math. Soc. 314 (1989), 661-692. Zbl0689.42016MR972707

1. Gladis Pradolini, Jorgelina Recchi, Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces