qiaozhen zhao

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In this paper, we establish sharp maximal function inequalities for the Toeplitz-type operator associated with the singular integral operator with a variable Calderón-Zygmund kernel. As an application, we obtain the boundedness of the operator on Lebesgue, Morrey and Triebel-Lizorkin spaces.


function inequalities; Toeplitz-type operator; singular integral operator.


Toeplitz type operator; Singular integral operator; Variable Calder´on-Zygmund Kernel; Sharp maximal function; Morrey space; Triebel-Lizorkin space; BMO; Lipschitz function.In this paper, we establish the sharp maximal function inequalities for the Toepl

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A. P. Calder´on and A. Zygmund, On singular integrals with variable kernels, Appl. Anal.,

(1978), 221-238.

S. Chanillo, A note on commutators, Indiana Univ. Math. J., 31(1982), 7-16.

R. R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in

several variables, Ann. of Math., 103(1976), 611-635.

G. Di FaZio and M. A. Ragusa, Commutators and Morrey spaces, Boll. Un. Mat. Ital.,

-A(7)(1991), 323-332.

G. Di Fazio and M. A. Ragusa, Interior estimates in Morrey spaces for strong solutions

to nondivergence form equations with discontinuous coefficients, J. Func. Anal.,

(1993), 241-256.

J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted norm inequalities and related

topics, North-Holland Math.,16, Amsterdam, 1985.

S. Janson, Mean oscillation and commutators of singular integral operators, Ark. Math.,

(1978), 263-270.

S. Krantz and S. Li, Boundedness and compactness of integral operators on spaces of

homogeneous type and applications, J. of Math. Anal. Appl., 258(2001), 629-641.

Y. Lin and S. Z. Lu, Toeplitz type operators associated to strongly singular integral

operator, Sci. in China(ser.A), 36(2006), 615-630.

L. Z. Liu, Interior estimates in Morrey spaces for solutions of elliptic equations and

weighted boundedness for commutators of singular integral operators, Acta Math. Scientia,

(B)(1)(2005), 89-94.

L. Z. Liu, The continuity for multilinear singular integral operators with variable

Calder´on-Zygmund kernel on Hardy and Herz spaces, Siberia Electronic Math. Reports,

(2005), 156-166.

L. Z. Liu, Good λ estimate for multilinear singular integral operators with variable

Calder´on-Zygmund kernel, Kragujevac J. of Math., 27(2005), 19-30.

L. Z. Liu, Weighted estimates of multilinear singular integral operators with variable

Calder´on-Zygmund kernel for the extreme cases, Vietnam J. of Math., 34(1)(2006),


S. Z. Lu, D. C. Yang and Z. S. Zhou, Oscillatory singular integral operators with

Calder´on-Zygmund kernels, Southeast Asian Bull. of Math., 23(1999), 457-470.

T. Mizuhara, Boundedness of some classical operators on generalized Morrey spaces, in

”Harmonic Analysis”, Proceedings of a conference held in Sendai, Japan, 1990, 183-189.

M. Paluszynski, Characterization of the Besov spaces via the commutator operator of

Coifman, Rochberg and Weiss, Indiana Univ. Math. J., 44(1995), 1-17.

J. Peetre, On convolution operators leaving L

p,λ-spaces invariant, Ann. Mat. Pura.

Appl., 72(1966), 295-304.

J. Peetre, On the theory of L

p,λ-spaces, J. Func. Anal., 4(1969), 71-87.

C. P´erez, Endpoint estimate for commutators of singular integral operators, J. Func.

Anal., 128(1995), 163-185.

C. P´erez and R. Trujillo-Gonzalez, Sharp weighted estimates for multilinear commutators,

J. London Math. Soc., 65(2002), 672-692.

E. M. Stein, Harmonic analysis: real variable methods, orthogonality and oscillatory

integrals, Princeton Univ. Press, Princeton NJ, 1993.

H. Xu and L. Z. Liu., Weighted boundedness for multilinear singular integral operator

with variable Calder´on-Zygmund kernel, African Diaspora J. of Math., 6(1)(2008), 1-12.



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