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1993 | 104 | 2 | 195-209
Tytuł artykułu

Weighted estimates for commutators of linear operators

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EN
Abstrakty
EN
We study boundedness properties of commutators of general linear operators with real-valued BMO functions on weighted $L^p$ 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.
Twórcy
  • Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003, U.S.A.
  • Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003, U.S.A.
  • Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003, U.S.A.
  • Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003, U.S.A.
  • Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Bibliografia
  • [1] J. Alvarez, An algebra of $L^p$-bounded pseudo-differential operators, J. Math. Anal. Appl. 94 (1983), 268-282.
  • [2] J. Alvarez and J. Hounie, Estimates for the kernel and continuity properties of pseudo-differential operators, Ark. Mat. 28 (1990), 1-22.
  • [3] J. Alvarez and M. Milman, $H^p$ continuity properties of Calderón-Zygmund-type operators, J. Math. Anal. Appl. 118 (1986), 63-79.
  • [4] J. Alvarez and M. Milman, Vector valued inequalities for strongly singular Calderón-Zygmund operators, Rev. Mat. Iberoamericana 2 (1986), 405-426.
  • [5] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, Boston 1988.
  • [6] S. Chanillo and A. Torchinsky, Sharp function and weighted $L^p$ estimates for a class of pseudo-differential operators, Ark. Mat. 24 (1986), 1-25.
  • [7] R. Coifman et Y. Meyer, Au delà des opérateurs pseudo-différentiels, Astérisque 57 (1978).
  • [8] R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. 103 (1976), 611-635.
  • [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.
  • [10] J. Duoandikoetxea, Weighted norm inequalities for homogeneous singular integrals, preprint.
  • [11] J. Duoandikoetxea and J. L. Rubio de Francia, Maximal and singular integral operators via Fourier transform estimates, Invent. Math. 84 (1986), 541-561.
  • [12] N. Dunford and J. Schwartz, Linear Operators, Part I, Wiley Interscience, New York 1958.
  • [13] C. Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 123 (1969), 9-36.
  • [14] C. Fefferman and E. M. Stein, $H^p$ spaces of several variables, ibid. 129 (1972), 137-193.
  • [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.
  • [16] S. Hofmann, Weighted norm inequalities and vector-valued inequalities for certain rough operators, preprint.
  • [17] L. Hörmander, Pseudo-differential operators and hypo-elliptic operators, in: Proc. Sympos. Pure Math. 10, Amer. Math. Soc., 1967, 138-183.
  • [18] J. Hounie, On the $L^2$ continuity of pseudo-differential operators, Comm. Partial Differential Equations 11 (1986), 765-778.
  • [19] R. A. Hunt and W.-S. Young, A weighted norm inequality for Fourier series, Bull. Amer. Math. Soc. 80 (1974), 274-277.
  • [20] S. Janson, Mean oscillation and commutators of singular integrals operators, Ark. Mat. 16 (1978), 263-270.
  • [21] T. Kato, Perturbation Theory for Linear Operators, Springer, 1976.
  • [22] D. S. Kurtz, Operator estimates using the sharp function, Pacific J. Math. 139 (1989), 267-277.
  • [23] D. S. Kurtz and R. L. Wheeden, Results on weighted norm inequalities for multipliers, Trans. Amer. Math. Soc. 255 (1979), 343-362.
  • [24] N. Miller, Weighted Sobolev spaces and pseudodifferential operators with smooth symbols, ibid. 269 (1982), 91-109.
  • [25] B. Muckenhoupt, R. L. Wheeden and W.-S. Young, Sufficiency conditions for $L^p$ multipliers with general weights, ibid. 300 (1987), 463-502.
  • [26] C. Neugebauer, Inserting $A_p$-weights, Proc. Amer. Math. Soc. 87 (1983), 644-648.
  • [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.
  • [28] E. Sawyer, Multipliers on Besov and power-weighted $L^2$ spaces, Indiana Univ. Math. J. 33 (1984), 353-366.
  • [29] E. M. Stein, Interpolation of linear operators, Trans. Amer. Math. Soc. 83 (1956), 482-492.
  • [30] J. O. Strömberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math. 1381, Springer, 1989.
  • [31] D. K. Watson, Weighted estimates for singular integrals via Fourier transform estimates, Duke Math. J. 60 (1990), 389-400.
  • [32] A. C. Zaanen, Interpolation, North-Holland, 1967.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv104i2p195bwm
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