Multipliers and Herz type spaces

Hrmander condition for boundedness of multiplier operators will be replaced by a weaker condition described by certain weighted or non-weighted Herz spaces. Some results on boundedness of multiplier operators are then established. As direct corollaries of main theorems in this paper, several celebrated results on boundedness of multiplier operators will be improved or deduced.     

加权Herz型Hardy空间上的Littlewood-Paley g函数

研究了Littlewood-Paley g函数gψ(f)(x)在加权Herz型Hardy空间上的性质,得到了如下结果,若ω1,ω2∈A1,则当n(1-1/q)≤α≤n(1-1/q) ε时,gψ为HK^a,p q(ω1,ω2)到K^a,p q(ω1,ω2)上的有界算子,当α＝n(1-1/) ω时,gψ为HK^a,p q(ω1,ω2）到WK^a,p q(ω1,ω2)上的有界算子。     

Herz型Hardy空间上的一类交换子

证明一大类次线性算子与ＢＭＯ函数构成的交换子在Ｈａｒｚ型Ｈａｒｄｙ空间上的有界性。     

次线性算子在加权Herz空间上的弱型估计

给出了一些次线性算子从加权Herz空间到加权弱Herz空间的有界性证明。     

Multiplier theorems for Herz type Hardy spaces

In this paper, the authors establish a multiplier theorem for Herz type Hardy spaces.

     

An oscillating multiplier on Herz type spaces

In this paper, the boundedness of an oscillating multiplier m γ,β for different β on the Herz type spaces is obtained. This operator was initially studied by Wainger and Fefferman-Stein. Our results extend one of the main results in a paper by Xiaochun Li and Shanzhen Lu for the non-weighted case, if β is close to 1 or α is suitably large. For β ≥ 1, the results with no weights on the Herz type spaces are also new.     

BOUNDEDNESS OF VECTOR-VALUED CALDERON-ZYGMUND OPERATORS ON HERZ SPACES WITH NON-DOUBLING MEASURES

In the paper we obtain vector-valued inequalities for Calderon-Zygmund operator,simply CZO On Herz space and weak Herz space.In particular,we obtain vector-valued inequalities for CZO on Lq(Rd,│x│αdμ)space,with 1＜q＜∞,-n＜α＜n(q-1),and on L1,∞(Rd,│x│αdμ)space,with -n＜α＜0.     

具有粗糙核的多线性算子在Herz型空间的有界性

§ 1　Introduction and main resultsLet b∈BMO(Rn) and T be a standard Calderon-Zygmund singular integral operator.Define the commutator[b,T] as follows.[b,T] f(x) =b(x) Tf(x) -T(bf) (x) .In [3 ] ,the boundedness ofthe commutator[b,T] wasestablished on Lp(Rn) .There are thesimilar results in [1 ,2 ] when the commutator was substituted with the multilinearoperators generated by the singular integral operator T and a Taylor series A(see thedefinition below) .Recently,many mathematicians h…     

一类次线性算子在加权Herz型Hardy空间上的有界性

得到了新Ｃａｌｄｅｒｏｎ－Ｚｙｈｍｕｎｄ算子的Ｈ Ｋ_ｑ~（ａ,ｐ）（ｗ_１;Ｗ_２到Ｋ_ｑ~（ａ,ｐ）（ｗ_１;ｗ_２）有界性和Ｈ Ｋ_ｑ~（ａ,ｐ）（１;ｘ~β）到ＨＫ_ｑ~（ａ,ｐ）（１;ｘ~β）有界性．     

Calderón-Zygmund operators on Herz type Hardy spaces

We consider the boundedness of Calderón-Zygmund operators from to , where is the Hardy space associated with the Herz space and is the local version of . We show Calderón's commutator is bounded from to .     

Boundedness for multilinear fractional integral operators on Herz type spaces

In this paper the boundedness for the multilinear fractional integral operator Iα^（m） on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators.     

Herz type Besov and Triebel-Lizorkin spaces with variable exponent

The Herz type Besov and Triebel-Lizorkin spaces with variable exponent are introduced. Then characterizations of these new spaces by maximal functions are given.     

一类分数次算子在加权Herz型Hardy空间上的有界性

证明了一类分数次算子的ＨＫ_ｑ_１~（ａ,ｐ）（ｗ_１;ｗ_２~ｑ１）到Ｋ_ｑ_２~（ａ,ｐ）（ｗ_１;ｗ_２~ｑ２）和ＨＫ_ｑ_１~ａ_１~ｐ（１,ｘ~（βｑ_１）到Ｋ_ｑ_２~ａ_１~ｐ（１,ｘ~（βｑ_２）的有界性．     

Besov spaces and Herz spaces on local fields

The relationship of Besov spaces and Herz spaces on local fields is given. As an application, one multiplier theorem is obtained. And the decompositional characterization of the weighted Besov spaces is established.     

Herz型空间

这是有关Herz型空间的综述报告，它是基于作者及其合作者近10年来的研究工作．这些工作包括分解定理、对偶空间、插值以及Herz型空间的某些应用．     

加权Herz型空间上次线性算子的弱有界性

研究了一类次线性算子在加权Herz空间.Knq(1-1/q),p(ω1;ω2)上的有界性.     

带粗糙核的Marcinkiewicz积分算子在Herz空间的有界性

本文考虑如下的Macinkiewicz积分算子μΩ（f）（x）{∫0^∞｜FΩ ,t（x）｜^2t^-3dt}^1/2,其中FΩ ,t（x）=∫｜x-y｜≤tΩ （x-y）｜x-y｜^-n＋2f（y）dy在一定的条件下证明它是在Herz空间Kq^α,q上有界同时也是从Herz空间K1^α,p到弱Herz空间WK1^α,p上有界。     

Boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents

We obtain the boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents K^˙α(?)_p(?,q(?)),such as some sublinear operators,the fractional integral and its commutator.     

Parameterized Littlewood-Paley Operators on Weighted Herz Spaces

The strong type and weak type estimates of parameterized Littlewood-Paley operators on the weighted Herz spaces K_q~(α,p) (ω_1, ω_2) are considered. The boundedness of the commutators generated by BMO functions and parameterized Littlewood-Paley operators are also obtained.     

次线性算子在Herz型Hardy空间上的有界性

本文得到了一类次线性算子在Herz型Hardy空间上的有界性判定条件,该算子包括调和分析中许多重要的算子,同时还证明了Bochner-Riesz算子在Herz型Hardy空间上的有界性.