1) (θ,0) type fractional operator
(θ,0)型分数次积分算子
2) θ-type Caldero n-Zygmund operator
θ-型Caldero'n-Zygmund奇异积分算子
3) θ(t)-type singular integral operators
θ(t)型奇异积分算子
1.
By using the atomic and molecular decompositions of Hp(Rn) which is an anisotropic Hardy space associated with a given expansive matrix A,the boundedness of θ(t)-type singular integral operators which is associated with A and is from the anisotropic hardy space H1(Rn) to L1(Rn) space or from Hp(Rn) to Hp(Rn) is researched.
对于伴随于一个扩张矩阵A的各向异性Hardy空间Hp(Rn),利用此空间的原子分解和分子分解,本文讨论了伴随于A的θ(t)型奇异积分算子在各向异性Hardy空间H1(Rn)到L1(Rn)空间的有界性,以及在各向异性Hardy空间Hp(Rn)自身上的有界性。
4) fractional integral operator
分数次积分算子
1.
Boundedness of the fractional integral operator in weak type Hardy space;
分数次积分算子在弱Hardy型空间中的有界性
2.
The boundedness of fractional integral operators with homogeneous kernel in weak type Hardy spaces is discussed when the kernel of the operators satisfies Dini condition.
讨论具有齐性核的分数次积分算子 ,当核函数满足 Dini条件时在弱 H1 ( IRn)上的有界性问
3.
In this paper, certain orlicz-Hardy-sobolev spaces H_k~φ(R~n)and H_s~φ(R~n)are defined byusing fractional integral operators I~s; then, it proves, under certain condition, that Hφ(R~n) is equivalent to H_k~φ(R_n) when k is a non-negative integer.
本文通过研究分数次积分算子对Orlicz-Hardy空间H_φ(R~n)的作用,引入了势空间H_s~φ(R~n),并给出了其等价刻划,同时证明在一定条件下,当k为整数时,H_k~φ(R~n)等价于Orlicz-Hardy-Sobolev空间H_k~φ(R~n)。
5) fractional integral
分数次积分算子
1.
The boundedness is established of the commutators generated by Calderón-Zygmund operators or fractional integrals with RBMO(μ) functions or Lipschitz functions in Morrey spaces on nonhomogeneous spaces.
证明了由Calderón-Zygmund算子或分数次积分算子与RBMO(μ)函数以及Lipschitz函数生成的交换子在非齐型空间上的Morrey空间中的有界性。
2.
Sufficient conditions are given for fractional integral operater I α to be bounded from weighted weak Legesgue spaces with some range p into another suitable weighted BMO and Lipschitz spaces of order β .
给出了分数次积分算子从加权Lebesgue空间到加权Lipschitz空间有界性的充分条件 ,同时给出了从加权BMO空间到加权Lipschitz空间有界性的充要条
3.
In this paper we prove the following conclusions:(1)the fractional integral operator I_l and maximal operator M_l are bounded from K_(q1)~(α,p1)(1,ωα)to W K_(q2)~(α,p2)(1,ωβ), where q1=1,0<p1≤1,p1≤p2,0<β<1,α=β(n-l)/n,q2=n/(n-l),0<l<n andω_α(x)=|x|_(-α).
本文我们证明了如下结论: (1)分数次积分算子I_l与分数次极大算子M_l是K_(q1)~(α,p1)(1,ωα)到WK~(q2)~(α,p2)(1,ωβ)中的有界算子,其中q1=1,0
6) fractional calculus operators
分数次微积分算子
1.
Using fractional calculus operators of order u,he gets the precise distortion theorems of analytic functions,which belon.
用Hadamard积(或卷积)定义积分算子In+p,并利用算子In+p与微分从属关系定义了p叶解析函数类Tn+p(η;A,B),给出函数f(z)属于类Tn+p(η;A,B)的充分必要条件,考虑类Tn+p(η;A,B)中的函数在u阶分数次微积分算子作用下的准确的偏差定理。
补充资料：积分算子
积分算子
integral operator
积分算子[加魄间0碑拍tor;抓，印~碱。.eP‘p〕 一个映射x巨Ax，其对应规则A由一个积分给定.积分算子有时称为积分变换(甸啡”1 tiansfor-mation).例如，对于yP~积分算子(见yp“仁洲方程(U够。加闪甲石的))中‘~A毋，其对应莎侧A由积分 A中(‘)二Jp(‘，T，中(T))d:，‘〔D(l) D给定(或此算子，一A中由该积分生成)，其中D是一个有限维空间中给定的具有有限u比脚测度的可测集，而p(r，;，u)(t，:〔D，一田
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