Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (5): 1093-1103.

• Articles • Previous Articles     Next Articles

λ-Center BMO Estimates for the Toeplitz Operator Related to Singular Integral Operator with Non-smooth Kernels

 CHEN Dong-Xiang, FANG Yu-Da   

  1. Department of Mathematics, Jiangxi Normal University, Nanchang 330022
  • Received:2013-03-11 Revised:2014-04-30 Online:2014-10-25 Published:2014-10-25
  • Supported by:

    国家自然科学基金(11326092, 11261023)、江西省自然科学基金(20122BAB201011)和江西省教育厅基金(GJJ1223)资助.

Abstract:

Let L be the infinitesimal generator of analytic semigroup on L2(Rn) with Gaussian kernel bounds, and L-α/2 be the general fractional integrals generated by L for 0<α<n. Let Tj,1 be the singular integral with non smooth kernel related to L, or Tj,1=I,Tj,2,Tj,4 be the linner operators, which are bounded on Lp(Rn) for 1<p<∞, and Tj,3I(j=1,2…, m), where I is the identity operator, Mb is a multiplication operator.  the authors prove that when  b∈CBMOp2,λ2, the Toeplitz-type operator
 θbα is bounded from Bp1, λto Bp1, λ1. As applications, the boundedness of the general fractional integral commutator
[b , L-α/2] on center Morrey space and that of the commutator of singular integral operator with non-smooth kernel [b, T] on center Morrey space are established.

Key words: Toeplitz type operator, Generalized fractional integral, Singular integral with nonsmooth kernel, λ-CBMO space

CLC Number: 

  • 42B25
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