• Previous Article
    Logarithmic and improved regularity criteria for the 3D nematic liquid crystals models, Boussinesq system, and MHD equations in a bounded domain
  • CPAA Home
  • This Issue
  • Next Article
    A note on the unique continuation property for fully nonlinear elliptic equations
March  2015, 14(2): 627-636. doi: 10.3934/cpaa.2015.14.627

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

1. 

Department of Mathematics, Hunan University, Changsha 410082, China

Received  January 2014 Revised  July 2014 Published  December 2014

In this paper, the boundedness from Lebesgue space to Orlicz space of certain Toeplitz type operator related to the pseudo-differential operator is obtained.
Citation: Lanzhe Liu. Mean oscillation and boundedness of Toeplitz Type operators associated to pseudo-differential operators. Communications on Pure & Applied Analysis, 2015, 14 (2) : 627-636. doi: 10.3934/cpaa.2015.14.627
References:
[1]

S. Chanillo, A note on commutators,, \emph{Indiana Univ. Math. J.}, 31 (1982), 7.  doi: 10.1512/iumj.1982.31.31002.  Google Scholar

[2]

S. Chanillo and A. Torchinsky, Sharp function and weighted $L^p$ estimates for a class of pseudo-differential operators,, \emph{Ark. for Mat.}, 24 (1986), 1.  doi: 10.1007/BF02384387.  Google Scholar

[3]

R. Coifman and Y. Meyer, Au delá des opérateurs pseudo-différentiels,, \emph{Ast\'erisque}, 57 (1978).   Google Scholar

[4]

R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables,, \emph{Ann. of Math.}, 103 (1976), 611.   Google Scholar

[5]

C. Fefferman, $L^p$ bounds for pseudo-differential operators,, \emph{Israel J. Math.}, 14 (1973), 413.   Google Scholar

[6]

J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics,, North-Holland Math., (1985).   Google Scholar

[7]

S. Janson, Mean oscillation and commutators of singular integral operators,, \emph{Ark. for Mat.}, 16 (1978), 263.  doi: 10.1007/BF02386000.  Google Scholar

[8]

S. Janson and J. Peetre, Paracommutators boundedness and Schatten-von Neumann properties,, \emph{Tran. Amer. Math. Soc.}, 305 (1988), 467.  doi: 10.2307/2000875.  Google Scholar

[9]

S. Janson and J. Peetre, Higher order commutators of singular integral operators,, Interpolation spaces and allied topics in analysis, (1070), 125.  doi: 10.1007/BFb0099097.  Google Scholar

[10]

L. Z. Liu, Sharp and weighted boundedness for multilinear operators associated with pseudo-differential operators on Morrey space,, \emph{J. of Contemporary Math. Analysis}, 45 (2010), 136.  doi: 10.3103/S1068362310030039.  Google Scholar

[11]

L. Z. Liu, Sharp maximal function inequalities and boundedness for Toeplitz type operator associated to pseudo-differential operator,, \emph{J. of Pseudo-Differential Operators and Applications}, 3 (2012), 329.  doi: 10.1007/s11868-012-0060-y.  Google Scholar

[12]

N. Miller, Weighted Sobolev spaces and pseudo-differential operators with smooth symbols,, \emph{Trans. Amer. Math. Soc.}, 269 (1982), 91.  doi: 10.2307/1998595.  Google Scholar

[13]

M. Paluszynski, Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss,, \emph{Indiana Univ. Math. J.}, 44 (1995), 1.  doi: 10.1512/iumj.1995.44.1976.  Google Scholar

[14]

C. Pérez and G. Pradolini, Sharp weighted endpoint estimates for commutators of singular integral operators,, \emph{Michigan Math. J.}, 49 (2001), 23.  doi: 10.1307/mmj/1008719033.  Google Scholar

[15]

C. Pérez and R. Trujillo-Gonzalez, Sharp weighted estimates for multilinear commutators,, \emph{J. London Math. Soc.}, 65 (2002), 672.  doi: 10.1112/S0024610702003174.  Google Scholar

[16]

M. Saidani, A. Lahmar-Benbernou and S. Gala, Pseudo-differential operators and commutators in multiplier spaces,, \emph{African Diaspora J. of Math.}, 6 (2008), 31.   Google Scholar

[17]

E. M. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality and Oscillatory Integrals,, Princeton Univ. Press, (1993).   Google Scholar

[18]

M. E. Taylor, Pseudo-differential Operators and Nonlinear PDE,, Birkhauser, (1991).   Google Scholar

show all references

References:
[1]

S. Chanillo, A note on commutators,, \emph{Indiana Univ. Math. J.}, 31 (1982), 7.  doi: 10.1512/iumj.1982.31.31002.  Google Scholar

[2]

S. Chanillo and A. Torchinsky, Sharp function and weighted $L^p$ estimates for a class of pseudo-differential operators,, \emph{Ark. for Mat.}, 24 (1986), 1.  doi: 10.1007/BF02384387.  Google Scholar

[3]

R. Coifman and Y. Meyer, Au delá des opérateurs pseudo-différentiels,, \emph{Ast\'erisque}, 57 (1978).   Google Scholar

[4]

R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables,, \emph{Ann. of Math.}, 103 (1976), 611.   Google Scholar

[5]

C. Fefferman, $L^p$ bounds for pseudo-differential operators,, \emph{Israel J. Math.}, 14 (1973), 413.   Google Scholar

[6]

J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics,, North-Holland Math., (1985).   Google Scholar

[7]

S. Janson, Mean oscillation and commutators of singular integral operators,, \emph{Ark. for Mat.}, 16 (1978), 263.  doi: 10.1007/BF02386000.  Google Scholar

[8]

S. Janson and J. Peetre, Paracommutators boundedness and Schatten-von Neumann properties,, \emph{Tran. Amer. Math. Soc.}, 305 (1988), 467.  doi: 10.2307/2000875.  Google Scholar

[9]

S. Janson and J. Peetre, Higher order commutators of singular integral operators,, Interpolation spaces and allied topics in analysis, (1070), 125.  doi: 10.1007/BFb0099097.  Google Scholar

[10]

L. Z. Liu, Sharp and weighted boundedness for multilinear operators associated with pseudo-differential operators on Morrey space,, \emph{J. of Contemporary Math. Analysis}, 45 (2010), 136.  doi: 10.3103/S1068362310030039.  Google Scholar

[11]

L. Z. Liu, Sharp maximal function inequalities and boundedness for Toeplitz type operator associated to pseudo-differential operator,, \emph{J. of Pseudo-Differential Operators and Applications}, 3 (2012), 329.  doi: 10.1007/s11868-012-0060-y.  Google Scholar

[12]

N. Miller, Weighted Sobolev spaces and pseudo-differential operators with smooth symbols,, \emph{Trans. Amer. Math. Soc.}, 269 (1982), 91.  doi: 10.2307/1998595.  Google Scholar

[13]

M. Paluszynski, Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss,, \emph{Indiana Univ. Math. J.}, 44 (1995), 1.  doi: 10.1512/iumj.1995.44.1976.  Google Scholar

[14]

C. Pérez and G. Pradolini, Sharp weighted endpoint estimates for commutators of singular integral operators,, \emph{Michigan Math. J.}, 49 (2001), 23.  doi: 10.1307/mmj/1008719033.  Google Scholar

[15]

C. Pérez and R. Trujillo-Gonzalez, Sharp weighted estimates for multilinear commutators,, \emph{J. London Math. Soc.}, 65 (2002), 672.  doi: 10.1112/S0024610702003174.  Google Scholar

[16]

M. Saidani, A. Lahmar-Benbernou and S. Gala, Pseudo-differential operators and commutators in multiplier spaces,, \emph{African Diaspora J. of Math.}, 6 (2008), 31.   Google Scholar

[17]

E. M. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality and Oscillatory Integrals,, Princeton Univ. Press, (1993).   Google Scholar

[18]

M. E. Taylor, Pseudo-differential Operators and Nonlinear PDE,, Birkhauser, (1991).   Google Scholar

[1]

Mostafa Mbekhta. Representation and approximation of the polar factor of an operator on a Hilbert space. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020463

[2]

Hirokazu Ninomiya. Entire solutions of the Allen–Cahn–Nagumo equation in a multi-dimensional space. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 395-412. doi: 10.3934/dcds.2020364

[3]

Zedong Yang, Guotao Wang, Ravi P. Agarwal, Haiyong Xu. Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020436

[4]

Lorenzo Zambotti. A brief and personal history of stochastic partial differential equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 471-487. doi: 10.3934/dcds.2020264

[5]

Adrian Constantin, Darren G. Crowdy, Vikas S. Krishnamurthy, Miles H. Wheeler. Stuart-type polar vortices on a rotating sphere. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 201-215. doi: 10.3934/dcds.2020263

[6]

Fabio Camilli, Giulia Cavagnari, Raul De Maio, Benedetto Piccoli. Superposition principle and schemes for measure differential equations. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020050

[7]

Siyang Cai, Yongmei Cai, Xuerong Mao. A stochastic differential equation SIS epidemic model with regime switching. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020317

[8]

Yueyang Zheng, Jingtao Shi. A stackelberg game of backward stochastic differential equations with partial information. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020047

[9]

Sumit Arora, Manil T. Mohan, Jaydev Dabas. Approximate controllability of a Sobolev type impulsive functional evolution system in Banach spaces. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020049

[10]

Meng Chen, Yong Hu, Matteo Penegini. On projective threefolds of general type with small positive geometric genus. Electronic Research Archive, , () : -. doi: 10.3934/era.2020117

[11]

Shun Zhang, Jianlin Jiang, Su Zhang, Yibing Lv, Yuzhen Guo. ADMM-type methods for generalized multi-facility Weber problem. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020171

[12]

Mengni Li. Global regularity for a class of Monge-Ampère type equations with nonzero boundary conditions. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020267

[13]

Thabet Abdeljawad, Mohammad Esmael Samei. Applying quantum calculus for the existence of solution of $ q $-integro-differential equations with three criteria. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020440

[14]

Xavier Carvajal, Liliana Esquivel, Raphael Santos. On local well-posedness and ill-posedness results for a coupled system of mkdv type equations. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020382

[15]

Fathalla A. Rihan, Hebatallah J. Alsakaji. Stochastic delay differential equations of three-species prey-predator system with cooperation among prey species. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020468

2019 Impact Factor: 1.105

Metrics

  • PDF downloads (39)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]