Two Weighted BMO Estimates for the Maximal Bochner-Riesz Commutator

In this note, the author prove that maximal Bocher-Riesz commutator Bδ,＊^b generated by operator Bδ,＊ and function b∈ BMO（ω） is a bounded operator from L^p（μ） into L^p（ν）, where w∈ （μν^- 1）^1/p,μ,v ∈ Ap for 1 〈 p 〈 ∞. The proof relies heavily on the pointwise estimates for the sharp maximal function of the commutator Bδ,＊^b.

Characterizations of Weighted BMO Space and Its Application

In this paper,we prove that the weighted BMO space BMO^(p)(ω)={f∈L^(1)_(loc):sup||χQ||^(-1)Lp(ω)||(F-Fq)ω^(-1)χQ||LP(ω)<∞Q}is independent of the scale p∈(0,∞)in sense of norm whenω∈A_(1).Moreover,we can replace L^(p)(ω)by L^(p,∞)(ω).As an application,we characterize this space by the boundedness of the bilinear commutators[b,T]_(j)(j=1,2),generated by the bilinear convolution type Calderdn-Zygmund operators and the symbol b,from L^(p1)(ω)×L^(p2)(ω)to L^(p)(ω^(1-p))with 1<p1,p2<∞and 1/p=1/p1+1/p2.Thus we answer the open problem proposed by Chaffee affirmatively.

Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces

Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.

Toeplitz Operator Related to Singular Integral with Non-Smooth Kernel on Weighted Morrey Space

Let T1 be a singular integral with non-smooth kernel or ±I, let T2 and T4 be the linear operators and let T3 = ± I. Denote the Toeplitz type operator by Tb = T1M^b Ia T2 ＋ T3IaMbT4,where M^bf = bf, and Ib is the fractional integral operator. In this paper, we investigate the boundedness of the operator Tb on the weighted Morrey space when b belongs to the weighted BMO space.

Boundedness for Commutators of Approximate Identities on Weighted Morrey Spaces

The aim of this paper is to set up the weighted norm inequalities for commutators generated by approximate identities from weighted Lebesgue spaces into weighted Morrey spaces

ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT A_p CLASS

This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces LP（w） to weighted Morrey spaces Mpq（ω） for 1 〈 q 〈 p 〈 ∞. As a corollary, if M is （weak） bounded on Mpq（ω）, then ω∈Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators Tε on weighted Morrey spaces. Finally, we show that ω∈Ap if and only if ω∈BMOp＇ （ω） for 1 ≤ p 〈 ∞ and 1/p ＋ 1/p＇ = 1.

Weighted Estimates for Commutators of Strongly Singular Calderón–Zygmund Operators

In this paper, the authors establish the boundedness of commutators generated by strongly singular CalderSn-Zygmund operators and weighted BMO functions on weighted Herz-type Hardy spaces. Moreover, the corresponding results for commutators generated by strongly singular CalderSn- Zygmund operators and weighted Lipschitz functions can also be obtained.

Weighted L^p Estimates for Maximal Commutators of Multilinear Singular Integrals

This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T∑b^＊ and TПb^＊ which are generalized by a weighted BMO function b and a multilinear singular integral operator T, respectively. As applications, some commutator theorems are established.