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A note on the unique continuation property for fully nonlinear elliptic equations
Mean oscillation and boundedness of Toeplitz Type operators associated to pseudo-differential operators
| 1. | Department of Mathematics, Hunan University, Changsha 410082, China |
References:
| [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. |
show all references
References:
| [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. |
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