变指标中心BMO空间

本文引进变指标中心有界平均振荡函数空间.作为应用,得到了Hardy算子及其共轭算子的交换子在变指标勒贝格空间上有界性的特征刻画.另外,还考虑了交换子在变指标Herz空间上的向量值不等式.     

The space for nondoubling measures in terms of a grand maximal operator

Let be a Radon measure on , which may be nondoubling. The only condition that must satisfy is the size condition , for some fixed . Recently, some spaces of type BMO(\mu)$"> and were introduced by the author. These new spaces have properties similar to those of the classical spaces BMO}$"> and defined for doubling measures, and they have proved to be useful for studying the boundedness of Calderón-Zygmund operators without assuming doubling conditions. In this paper a characterization of the new atomic Hardy space in terms of a maximal operator is given. It is shown that belongs to if and only if , and , as in the usual doubling situation.

     

L^2（R^n） Boundedness for a Class of Multilinear Singular Integral Operators

The L^2(R^n) boundedness for the multilinear singular integral operators defined by TAf(x)=∫R^nΩ（x-y）/|x-y|^n 1(A(x)-A(y)-△↓A(y)(x-y))f(y)dy is considered,where Ω is homogeneous of degree zero,integrable on the unit sphere and has vanishing moment of order one,A has derivatives of order one in BMO(R^n） boundedness for the multilinear operator TA is given.     

BMO spaces related to Laguerre semigroups

For the system of Laguerre functions we define a suitable BMO space from the atomic version of the Hardy space considered by Dziubański in 7 , where is the maximal operator of the heat semigroup associated to that Laguerre system. We prove boundedness of over a weighted version of that BMO, and we extend such result to other systems of Laguerre functions, namely and . To do that, we work with a more general family of weighted BMO‐like spaces that includes those associated to all of the above mentioned Laguerre systems. In this setting, we prove that the local versions of the Hardy‐Littlewood and the heat‐diffusion maximal operators turn to be bounded over such family of spaces for weights. This result plays a decisive role in proving the boundedness of Laguerre semigroup maximal operators.     

Some of Commutators on Spaces of Homogeneous Type

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｌｅｔａｂｅａｍｅａｓｕｒａｂｌｅｆｕｎｃｔｉｏｎ ,ｂｅａ φ∈Ｓ(Ｒ)ｎｏｎｎｅｇａｔｉｖｅｆｕｎｃｔｉｏｎ ,ａｎｄ 0 <ｒ <∞ .Ｄｅｆｉｎｅｃｏｍｍｕｔａｔｏｒｓａｓｆｏｌｌｏｗｓ :Ｃｒａ( ｆ) (ｘ) =ｓｕｐｘ∈Ｑ1｜Ｑ｜∫Ｑ｜ａ(ｘ) -ａ( ｙ) ｜ｒ｜ｆ( ｙ) ｜ｄｙ ,( 1 .1 )ａｎｄΦｒａ( ｆ) (ｘ) =ｓｕｐε>0∫Ｒｎ｜ａ(ｘ) -ａ( ｙ) ｜ｒφε( ｜ｘ- ｙ｜)｜ｆ( ｙ) ｜ｄｙ ,( 1 .2 )ｗｈｅｒｅＱｄｅｎｏｔｅｓａｃｕｂｅａｎｄφε(ｔ) =1εｎφ ｔε .Ｔｈｅｓｅｔｗｏｏｐｅｒａｔ…     

Toeplitz operators related to strongly singular Calderón-Zygmund operators

In this paper, the boundedness of Toeplitz operator Tb(f) related to strongly singular Calderon-Zygmund operators and Lipschitz function b∈Λβ0(Rn) is discussed from Lp(Rn) to Lq(Rn), 1/q=1/p-β0/n, and from Lp(Rn) to Triebel-Lizorkin space Fβ0,∞p. We also obtain the boundedness of generalized Toeplitz operatorθbα0 from LP(Rn) to Lq(Rn), 1/q =1/p-α0 β0/n. All the above results include the corresponding boundedness of commutators. Moreover, the boundedness of Toeplitz operator Tb(f) related to strongly singular Calderon-Zygmund operators and BMO function b is discussed on LP(Rn), 1 < p <∞.     

Pointwise estimates for the maximal multilinear singular integral operators

Two pointwise estimates relating the maximal multilinear singular integral operators and some classical maximal operators are established. These pointwise estimates imply the rearrangement estimate and the BLO(Rn) estimate for the maximal multilinear singular integral operators.     

L^p（R^n） Boundedness for the Maximal Operator of Multilinear Singular Integrals with Calderon-Zygmund Kernels

In this paper, the authors consider a class of maximal multilinear singular integral operators and maximal multilinear oscillatory singular integral operators with standard Calderón–Zygmund kernels, and obtain their boundedness on L ^p (ℝ ⁿ ) for 1 < p < ∞. Research supported by Professor Xu Yuesheng’s Research Grant in the program of "One hundred Distinguished Young Scientists" of the Chinese Academy of Sciences     

BOUNDEDNESS OF COMMUTATORS OF FRACTIONAL INTEGRATION ON HERZ-TYPE SPACES

1 IntroductionLgt b E BMO(Rn) and 11 be a fractional integration with 0 < I < n. The commutator[b, II] generated by b and 11 is defined by[b, II]f(x) = b(x)llf(x) ~ II(sf)(x).S.Chanillolz] stated that the operator [b, II] is a bounded operator from LPI (R") on LPZ(R")for 1/Pz = 1/pl -- l/n and 1 < pl < n/l. Recently, Lu Shanzhen and Yang Dachun[9] studiedthe commutator [b,ll] on Herz spaces and a new class of Herz-type Hardy spaces introducedby them and established the correspondi…     

BMO Spaces and John-Nirenberg Estimates for the Heisenberg Group Targets

In this paper, the BMO spaces for the Heisenberg group targets are studied. Some properties of the BMO spaces and the John-Nirenberg estimates are obtained.