Abstract
The authors establish the boundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions. In particular, the Calderón-Zygmund singular integrals and the rough R. Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered.
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Lu, S. Z. and Yang, D., The Decomposition of Weighted Herz Space onR n and its Applications, Science in China, Ser. A, 38(1995), 147–158.
Stein, E. M., Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals. Princeton Univ. Press, Princeton, N. J., 1993.
Stein, E. M., Note on Singular Integrals, Proc. Amer. Math. Soc., 8(1957), 250–254.
Soria, F. and Weiss, G., A Remark on Singular Integrals and Power Weights, Indiana Univ. Math., J., 43(1994), 187–204.
Coifman, R. R., Rochberg, R. and Weiss, G., Fractorization Theorems for Hardy Spaces in Several Variable, Ann. of Math., 103(1976), 611–635.
Lu, S. Z. & Yang, D., The Continuity of Commutators on Herz-Type Spaces, Michigan Math. J., 44(1997), 255–281.
Jiang, Y. S., Tang, L. & Yang, D., Continuity of Commutators on Weighted Herz-Type Spaces, Kyushu J. Math., 53(1999), 245–263.
Hu, G., Lu, S. Z. & Yang, D., Boundedness of Rough Singular Integral Operators on Herz Spaces, J. Austral. Math. Soc. (Series A), 66(1999), 201–223.
Tang, L., Jiang, Y., & Lu, S. Z., Sublinear Operators on Weighted Herz Spaces, J. Beijing Normal Univ. (Natural Science), 35(1999), 167–173.
Lu, S. Z., Tang, L., Yang, D., Boundedness of Commutators on Homogeneous Herz Spaces, Science in China, Ser. A, 41(1998), 1023–1033.
Muckenhoupt B. & Wheeden, R. L., Weighted Norm Inequalities for Singular and Fractional Integrals, Trans. Amer. Math. Soc., 161(1971), 249–258.
Garcia-Cuerva J. & Rubio de Francia, J. L., Weighted Norm Inequalities and Related Topics, North-Holland Math. Studies, Vol. 16, North-Holland, Amsterdam, 1985.
Hu, G., Weighted Norm Inequalities for Commutators of Homogeneous Singular Integrals, Acta Math. Sinica (New Ser.), 11(1995), 77–88.
Alvarez, J., Babgy, R. J., Kurtz, D. S. & Pérez, C., Weighted Estimate for Commutators of Linear Operators, Studia Math., 104(1993), 195–209.
Watson, D., Weighted Estimates for Singular Integrals Via Fourier Transform Estimates, Duke Math. J., 60(1990), 389–399.
Jiang, Y. S. and Lu, S. Z., Oscillatory Singular Integral with Rough Kernel, Harmonic Analysis in China, Kluwer Academic Publishers, the Netherlands, 1995, 135–145.
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Project 19871071 supported by Natural Science Foundation of China.
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Yinsheng, J., Mingju, L. Rough operators and commutators on homogeneous weighted Herz spaces. Approx. Theory & its Appl. 18, 51–67 (2002). https://doi.org/10.1007/BF02837048
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DOI: https://doi.org/10.1007/BF02837048