We study boundedness properties of commutators of general linear operators with real-valued BMO functions on weighted spaces. We then derive applications to particular important operators, such as Calderón-Zygmund type operators, pseudo-differential operators, multipliers, rough singular integrals and maximal type operators.
@article{bwmeta1.element.bwnjournal-article-smv104i2p195bwm, author = {Josefina Alvarez and Richard Bagby and Douglas Kurtz and Carlos P\'erez}, title = {Weighted estimates for commutators of linear operators}, journal = {Studia Mathematica}, volume = {104}, year = {1993}, pages = {195-209}, zbl = {0809.42006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv104i2p195bwm} }
Alvarez, Josefina; Bagby, Richard; Kurtz, Douglas; Pérez, Carlos. Weighted estimates for commutators of linear operators. Studia Mathematica, Tome 104 (1993) pp. 195-209. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv104i2p195bwm/
[00000] [1] J. Alvarez, An algebra of -bounded pseudo-differential operators, J. Math. Anal. Appl. 94 (1983), 268-282. | Zbl 0519.35084
[00001] [2] J. Alvarez and J. Hounie, Estimates for the kernel and continuity properties of pseudo-differential operators, Ark. Mat. 28 (1990), 1-22. | Zbl 0713.35106
[00002] [3] J. Alvarez and M. Milman, continuity properties of Calderón-Zygmund-type operators, J. Math. Anal. Appl. 118 (1986), 63-79. | Zbl 0596.42006
[00003] [4] J. Alvarez and M. Milman, Vector valued inequalities for strongly singular Calderón-Zygmund operators, Rev. Mat. Iberoamericana 2 (1986), 405-426. | Zbl 0634.42016
[00004] [5] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, Boston 1988. | Zbl 0647.46057
[00005] [6] S. Chanillo and A. Torchinsky, Sharp function and weighted estimates for a class of pseudo-differential operators, Ark. Mat. 24 (1986), 1-25. | Zbl 0609.35085
[00006] [7] R. Coifman et Y. Meyer, Au delà des opérateurs pseudo-différentiels, Astérisque 57 (1978). | Zbl 0483.35082
[00007] [8] R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. 103 (1976), 611-635. | Zbl 0326.32011
[00008] [9] R. L. Combs, Weighted norm inequalities with general weights for multipliers on functions with vanishing moments, Ph.D. thesis, New Mexico State Univ., Las Cruces, N.Mex., 1991.
[00009] [10] J. Duoandikoetxea, Weighted norm inequalities for homogeneous singular integrals, preprint. | Zbl 0770.42011
[00010] [11] J. Duoandikoetxea and J. L. Rubio de Francia, Maximal and singular integral operators via Fourier transform estimates, Invent. Math. 84 (1986), 541-561. | Zbl 0568.42012
[00011] [12] N. Dunford and J. Schwartz, Linear Operators, Part I, Wiley Interscience, New York 1958. | Zbl 0084.10402
[00012] [13] C. Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 123 (1969), 9-36. | Zbl 0188.42601
[00013] [14] C. Fefferman and E. M. Stein, spaces of several variables, ibid. 129 (1972), 137-193. | Zbl 0257.46078
[00014] [15] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. Stud. 116, North-Holland, Amsterdam 1985.
[00015] [16] S. Hofmann, Weighted norm inequalities and vector-valued inequalities for certain rough operators, preprint. | Zbl 0804.42010
[00016] [17] L. Hörmander, Pseudo-differential operators and hypo-elliptic operators, in: Proc. Sympos. Pure Math. 10, Amer. Math. Soc., 1967, 138-183.
[00017] [18] J. Hounie, On the continuity of pseudo-differential operators, Comm. Partial Differential Equations 11 (1986), 765-778. | Zbl 0597.35121
[00018] [19] R. A. Hunt and W.-S. Young, A weighted norm inequality for Fourier series, Bull. Amer. Math. Soc. 80 (1974), 274-277. | Zbl 0283.42004
[00019] [20] S. Janson, Mean oscillation and commutators of singular integrals operators, Ark. Mat. 16 (1978), 263-270. | Zbl 0404.42013
[00020] [21] T. Kato, Perturbation Theory for Linear Operators, Springer, 1976. | Zbl 0342.47009
[00021] [22] D. S. Kurtz, Operator estimates using the sharp function, Pacific J. Math. 139 (1989), 267-277. | Zbl 0646.42014
[00022] [23] D. S. Kurtz and R. L. Wheeden, Results on weighted norm inequalities for multipliers, Trans. Amer. Math. Soc. 255 (1979), 343-362. | Zbl 0427.42004
[00023] [24] N. Miller, Weighted Sobolev spaces and pseudodifferential operators with smooth symbols, ibid. 269 (1982), 91-109. | Zbl 0482.35082
[00024] [25] B. Muckenhoupt, R. L. Wheeden and W.-S. Young, Sufficiency conditions for multipliers with general weights, ibid. 300 (1987), 463-502. | Zbl 0641.42011
[00025] [26] C. Neugebauer, Inserting -weights, Proc. Amer. Math. Soc. 87 (1983), 644-648.
[00026] [27] J. L. Rubio de Francia, F. J. Ruiz and J. L. Torrea, Calderón-Zygmund theory for operator valued kernels, Adv. in Math. 62 (1986), 7-48. | Zbl 0627.42008
[00027] [28] E. Sawyer, Multipliers on Besov and power-weighted spaces, Indiana Univ. Math. J. 33 (1984), 353-366. | Zbl 0546.42011
[00028] [29] E. M. Stein, Interpolation of linear operators, Trans. Amer. Math. Soc. 83 (1956), 482-492. | Zbl 0072.32402
[00029] [30] J. O. Strömberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math. 1381, Springer, 1989.
[00030] [31] D. K. Watson, Weighted estimates for singular integrals via Fourier transform estimates, Duke Math. J. 60 (1990), 389-400. | Zbl 0711.42025
[00031] [32] A. C. Zaanen, Interpolation, North-Holland, 1967.