设 μΩ,α 为分数型Marcinkiewicz算子,[b,μΩ,α]是由μΩ,α 和有界平均振动(BMO)函数b(x)生成的交换子.利用Sharp极大函数估计以及空间分解理论,证明了 μΩ,α 和[b,μΩ,α]在加权Morrey空间上的有界性质.此外,考虑了 μΩ,α 在加权Morrey空间上的弱型估计.

利用变分法将证明方程解的存在性转化为求方程对应的能量泛函的临界点,得到了Kirchhoff-Schr?dinger-Poisson系统无穷多个非平凡解的存在性.

利用特征函数和空间分解原理对算子进行了估计.当指数满足pn--n+α<0,nγi-αi<0时,证明了多线性Marcinkiewicz算子与有界平均振动(BMO)函数生成的高阶交换子在变指数Herz-Morrey空间上的有界性.该结果也是经典Marcinkiewicz交换子在变指数Herz-Morrey空间上的推广.

研究了多线性Marcinkiewicz算子在变指数Herz-Morrey空间上的有界性,也是经典Marcinkiewicz算子在变指数Herz-Morrey空间上的推广.使用特征函数和空间分解原理,将算子分为4个部分,核函数所满足的尺寸条件,对算子进行估计,得到算子在变指数Herz-Morrey空间上的有界性.

为了研究Dini型多线性Calderón-Zygmund算子在Herz型Hardy空间上的有界性,通过对空间进行环状分解,利用中心原子对Herz型Hardy空间进行特征分解,再利用原子的消失性条件得到衰减估计,从而叠加得到结论.证明了当 α>n(1-1/q)时,Dini型多线性Calderón-Zygmund算子是从Herz型Hardy空间到Herz空间是有界的.

The boundedness of the commutator [b,T] was studied in the weighted Morrey space. When T are θ-type Calderón-Zygmund operators and b the weighted Campanato function, the commutator [b,T] is bounded on the weighted Morrey spaces by way of the maximal function estimation.

将交换子中的函数b由加权Lipschitz空间推广到加权Campanato空间,使用Sharp极大函数,证明了带变量核的Marcinkiewicz积分算子 μΩ 和某一类加权Campanato空间的函数b生成的交换子μbΩ 是由Lp(ω)到Lq(ω1-q)的有界算子,从而使用范围更广.

Suppose that L-p,L- kappa (w) is a weighted Morrey space in R-n. We establish two-weighted norm inequalities onweightedMorrey spaces for Hilbert and Riesz transforms. Moreover, with the assumption p > n, the C-Z singular integral operator is also established for two-weighted norm inequalities on weighted Morrey spaces.

In non-doubling measures, the boundedness of Marcinkiewicz integral operator M is investigated on weighted Morrey spaces. When weight function ω satisfies the condition of Ap (μ) , the operators M is bounded from Lp,k (ω) to weak Lp,k (ω), where 1≤p<∞,0<k<1. It mainly generalizes the result of Marcinkiewicz integral operator in non-doubling measures.

Let L~(p,k)(ω) be the weighted Morrey spaces,suppose Tand I_αare CalderonZygmund integral operator and fractional integral operator and BMO function b.In this paper,if p=1 we discuss the commutators[b,T]and[b,I_α]are bounded from L~(Φ,k)(ω) to weak L~(1,k)(ω)(L~(q,k)(ω)),where Φ(t)=t log(e+t),1/q=1-α/n.

In this paper, by means of the theory of singular integrals and linear commutators, we establish the regularity in grand Money spaces of the solution to an elliptic equation in nondivergence form with VMO coefficients.

It is shown that the strongly singular Calderón-Zygmund operators and their commutators are bounded in weighted Morrey spaces.

Let θ(t) be a modulus of continuity.Suppose T is a singular integral operator with θ-type Calderón-Zygmund kernel.If w Ap,1<p<$,by using the extrapolation theory and decomposition of space,we obtain that the operator T is bounded in weighted Morrey space.That is,T is bounded from Lp,,κ(w) to Lp,κ(w).

Under the assumption that μ is a non-doubling measure on Rd,this paper studies the boundedness of Marcinkiewicz integrals and commutators generated by Marcinkiewicz integrals with RBMO(μ)functions on generalized Morrey spaces of non-homogeneous spaces.The result extends the conclusion of Y.Sawano.

In the setting of upper doubling measure metric space,this paper analyzes the Lipschitz spaces and equivalent conditions.Furthermore,it explores the boundedness of the Calderón-Zygmund operator,fractional integral operator and hypersingular integral operator in Lipschitz spaces.

Letω_i(x,r)(i=1,2) be a positive measurable function in R~n×R~+.If(ω_1,ω_2)∈S_(0,n),then the commutators generated by the BMO function and maximal operators M are bounded from L~(p,ω_1)(R~n) to L~(p,ω_2)(R~n).Similarly,the commutators generated by the singular integral operator T and the Riesz potential operator I_αare also bounded on generalized Morrey spaces.All the results generalize the corresponding results of Mizuhara on the generalized Morrey spaces.

设齐次空间(X,p,μ)上定义一类极大Morrey空间Lp),θ,λ(X,μ).此类极大Morrey空间是经典的Morrey空间和极大Lebesgue空间的推广.本文考虑了C-Z积分算子、位势算子与BMO函数生成的交换子在该类极大Morrey空间上的有界性.事实上,这些结果甚至在一般的欧式空间上也是新颖的.

It define the multilinear singular integral operators ,[j=1,…,l]are some functions on ,set [A=A1,…,Al],if [DαAj∈BMORn],then we obtain the boundedness of multilinear singular integral operators on generalized Morrey spaces.

When the kernel K(x,y) satisfies much higher strongly near the x=y,it shows that the strongly singular Calderón-zygmund integral operator and its commutatorare bounded in some kinds of Hardy-type space Hpbm,s(Rn) where the b is a Lipschitz function.

In order to solve the boundedness problem of the θ(t)-type Calderon-Zygmund integral operator in lipschitz spaces, a θ(t)-type kernel in place of a standard singular integral kernel is used, when μ is non doubling measures it could get that the following two statements are equivalent: a) ‖T(subscript e)1‖Λ(subscript β)≤c1; T(subscript e):Λ(subscript β)→Λ(subscript β) are bounded and‖T(subscript e)1‖(subscript Λ(subscript β)→Λ(subscript β)≤c2