Article Contents
Article Contents

# Mean oscillation and boundedness of Toeplitz Type operators associated to pseudo-differential operators

• In this paper, the boundedness from Lebesgue space to Orlicz space of certain Toeplitz type operator related to the pseudo-differential operator is obtained.
Mathematics Subject Classification: Primary: 42B20; Secondary: 42B25.

 Citation:

•  [1] S. Chanillo, A note on commutators, Indiana Univ. Math. J., 31 (1982), 7-16.doi: 10.1512/iumj.1982.31.31002. [2] S. Chanillo and A. Torchinsky, Sharp function and weighted $L^p$ estimates for a class of pseudo-differential operators, Ark. for Mat., 24 (1986), 1-25.doi: 10.1007/BF02384387. [3] R. Coifman and Y. Meyer, Au delá des opérateurs pseudo-différentiels, Astérisque, 57 (1978). [4] R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math., 103 (1976), 611-635. [5] C. Fefferman, $L^p$ bounds for pseudo-differential operators, Israel J. Math., 14 (1973), 413-417. [6] J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math., 116, Amsterdam, 1985. [7] S. Janson, Mean oscillation and commutators of singular integral operators, Ark. for Mat., 16 (1978), 263-270.doi: 10.1007/BF02386000. [8] S. Janson and J. Peetre, Paracommutators boundedness and Schatten-von Neumann properties, Tran. Amer. Math. Soc., 305 (1988), 467-504.doi: 10.2307/2000875. [9] S. Janson and J. Peetre, Higher order commutators of singular integral operators, Interpolation spaces and allied topics in analysis, Lecture Notes in Math., 1070, Springer, Berlin, 1984, 125-142.doi: 10.1007/BFb0099097. [10] L. Z. Liu, Sharp and weighted boundedness for multilinear operators associated with pseudo-differential operators on Morrey space, J. of Contemporary Math. Analysis, 45 (2010), 136-150.doi: 10.3103/S1068362310030039. [11] L. Z. Liu, Sharp maximal function inequalities and boundedness for Toeplitz type operator associated to pseudo-differential operator, J. of Pseudo-Differential Operators and Applications, 3 (2012), 329-350.doi: 10.1007/s11868-012-0060-y. [12] N. Miller, Weighted Sobolev spaces and pseudo-differential operators with smooth symbols, Trans. Amer. Math. Soc., 269 (1982), 91-109.doi: 10.2307/1998595. [13] M. Paluszynski, Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss, Indiana Univ. Math. J., 44 (1995), 1-17.doi: 10.1512/iumj.1995.44.1976. [14] C. Pérez and G. Pradolini, Sharp weighted endpoint estimates for commutators of singular integral operators, Michigan Math. J., 49 (2001), 23-37.doi: 10.1307/mmj/1008719033. [15] C. Pérez and R. Trujillo-Gonzalez, Sharp weighted estimates for multilinear commutators, J. London Math. Soc., 65 (2002), 672-692.doi: 10.1112/S0024610702003174. [16] M. Saidani, A. Lahmar-Benbernou and S. Gala, Pseudo-differential operators and commutators in multiplier spaces, African Diaspora J. of Math., 6 (2008), 31-53. [17] E. M. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality and Oscillatory Integrals, Princeton Univ. Press, Princeton NJ, 1993. [18] M. E. Taylor, Pseudo-differential Operators and Nonlinear PDE, Birkhauser, Boston, 1991.