Weighted boundedness for Toeplitz type operatorassociated to singular integral operator withvariable Calderón-Zygmund kernel

References (1)

1. S. Bloom,A commutator theorem and weightedBM O, Trans. Amer. Math. Soc.292,103–122, 1985. [2]A.P. Calderón and A. Zygmund,On singular integrals with variable kernels, Appl.Anal.7, 221–238, 1978. [3]S. Chanillo,A note on commutators, Indiana Univ. Math. J.31, 7-16, 1982. [4]R. Coifman and R. Rochberg,Another characterization of BMO, Proc. Amer. Math.Soc.79, 249–254, 1980. [5]R.R. Coifman, R. Rochberg, and G. Weiss,Factorization theorems for Hardy spacesin several variables, Ann. of Math.103, 611–635, 1976. [6]G. Di FaZio and M.A. Ragusa,Commutators and Morrey spaces, Boll. Un. Mat. Ital.5-A(7), 323–332, 1991. [7]G. Di Fazio and M.A. Ragusa,Interior estimates in Morrey spaces for strong solutionsto nondivergence form equations with discontinuous coefficients, J. Funct. Anal.112,241–256,1993. [8]J. Garcia-Cuerva,WeightedHpspaces, Dissertationes Math.162, 63 pp., 1979. [9]J. Garcia-Cuerva and J.L. Rubio de Francia,Weighted norm inequalities and relatedtopics, North-Holland Mathematics Studies,116, Amsterdam, 1985. [10]Y. X. He and Y. S. Wang,Commutators of Marcinkiewicz integrals and weightedBMO, Acta Math. Sinica (Chinese Series),54, 513–520, 2011. [11]B. Hu and J. Gu,Necessary and sufficient conditions for boundedness of some com-mutators with weighted Lipschitz functions, J. Math. Anal. Appl.340, 598–605, 2008. [12]S. Janson,Mean oscillation and commutators of singular integral operators, Ark.Math.16, 263–270, 1978. [13]Y. Komori and S. Shirai,Weighted Morrey spaces and a singular integral operator,Math. Nachr.282, 219–231, 2009. [14]S. Krantz and S. Li,Boundedness and compactness of integral operators on spaces ofhomogeneous type and applications, J. Math. Anal. Appl.258, 629–641, 2001. [15]Y. Lin and S.Z. Lu,Toeplitz type operators associated to strongly singular integraloperator, Sci. in China (ser. A Mathematics),36, 615–630, 2006. [16]L.Z. Liu,Interior estimates in Morrey spaces for solutions of elliptic equations andweighted boundedness for commutators of singular integral operators, Acta Math. Sci-entia25(B), 89–94, 2005. [17]L.Z. Liu,The continuity for multilinear singular integral operators with variableCalderón-Zygmund kernel on Hardy and Herz spaces, Siberia Elec. Math. Rep.2,156–166, 2005. [18]L.Z. Liu,Goodλestimate for multilinear singular integral operators with variableCalderón-Zygmund kernel, Kragujevac J. Math.7, 19–30, 2005. [19]L.Z. Liu,Weighted estimates of multilinear singular integral operators with variableCalderón-Zygmund kernel f