双线性分数次积分算子交换子在Morrey空间上有界的充分必要条件

In this paper,we obtain that b∈ BMO(R~n) if and only if the commutator[b,I_α]is bounded from the Morrey spaces L~(p_1,λ_1)(R~n)×L~(p_2,λ_2)(R~n) to L~(q,λ)(R~n),for some appropriate indices p,q,λ,μ.Also we show that b ∈ Lip_β(R~n) if and only if the commutator[b,I_α]is bounded from the Morrey spaces L~(p_1,λ_1)(R~n)×L~(p_2,λ_2)(R~n) to L~(q,λ)(R~n),for some appropriate indices p,q,λ,μ.     

与非光滑核的奇异积分算子的Toeplitz算子的λ-中心BMO估计

设L是L~2(R~n)上的一个解析半群的无穷小生成元,核函数满足高斯上界.L~(-α/2)(0αn)是由L生成的广义分数次积分算子,若T_(j,1)是与L有关的带有非光滑核的奇异积分算子,或T_(j,1)=I,T_(j,2),T_(j,4)是线性算子且具有(B~(p,λ),B~(p,λ))有界性(1p∞,λ∈R),T_(j,3)=±I(j=1,2,…,m),其中I为恒等算子,M_b是乘法算子.当b∈CBMO~(p_2,λ_2)函数时,证明Toeplitz型算子θ_a~b是B~(p_1,λ_1)到B~(q,λ)上的有界算子,并由此得广义分数次积分交换子[b,L~(-a/2)]和非光滑核的奇异积分交换子[b,T]在中心Morrey型空间上的有界性.     

Weighted Compact Commutator of Bilinear Fourier Multiplier Operator

Let T_σ be the bilinear Fourier multiplier operator with associated multiplier σ satisfying the Sobolev regularity that sup κ∈Z∥σ_κ∥W~s(R~(2n)) ∞ for some s ∈ (n, 2n]. In this paper, it is proved that the commutator generated by T_σ and CMO(R~n) functions is a compact operator from L~(p1)(R~n, w_1) × L~(p2)(R~n, w_2) to L~p(R~n, ν_w) for appropriate indices p_1, p_2, p ∈ (1, ∞) with1 p=1/ p_1 +1/ p_2 and weights w_1, w_2 such that w = (w_1, w_2) ∈ A_(p/t)(R~(2n)).     

带粗糙核的参数型Marcinkiwicz积分交换子在齐次Morrey-Herz空间上的有界性

本文研究一类带粗糙核的参数型Marcinkiwicz积分算子与BMO(R~n)函数生成的交换子μ_(?,b)~ρ在齐次Morrey-Herz空间MK˙_(p,q)~(α,λ)(R~n)上的有界性,利用经典调和分析的方法和实变技巧,证明了μ_(?,b)~ρ是从MK˙_(p,q)~(α,λ)(R~n)到MK˙_(p,q)~(α,λ)(R~n)上有界的.     

带非光滑核的多线性Marcinkiewicz积分的加权界

我们引入了带非光滑核的多线性Marcinkiewicz积分算子.设p_1,…,p_m∈(1,∞)和p∈(0,+∞)满足1/p_1+…+1/p_m=1/p,记P=(p_1,…,p_m),又设向量权ω=(ω_1,…,ω_m)∈A_p和v_ω=Π_(k=1)~mω_k~(p/pk),得到了Marcinkiewicz积分算子从L~(p_1)(ω_1)×…×L~(p_m)(ω_m)到L~p(v_ω)的常数界.     

乘子算子及其交换子在Morrey空间上的有界性

证明了乘子算子(M_p~q(R~n),Lip(β-n/q))的有界性和(M_p~q(R~n),BMO(R~n))的有界性.还得到乘子算子及其交换子在广义Morrey空问Lp,L_(p,φ)(R~n)上的有界性.     

Characterizations of Weighted BMO Space and Its Application

In this paper, we prove that the weighted BMO space■is independent of the scale p ∈(0, ∞) in sense of norm when ω∈ 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 Calderón–Zygmund operators and the symbol b, from L~(p1)(ω) × L~(p2)(ω) to L~p(ω~(1-p)) with 1 p_1, p_2 ∞ and 1/p = 1/p_1 + 1/p_2.Thus we answer the open problem proposed by Chaffee affirmatively.     

Commutators of Singular Integral Operators Related to Magnetic Schrdinger Operators

Let A:=-(▽-ia(向量))·(?-ia(向量))+V be a magnetic Schrdinger operator on L~2(R~n),n≥2,where a(向量)=(a_1,···,a_n)∈L~2_(loc)(R~n,R~n) and 0≤V∈L~1_(loc)(R~n).In this paper,we show that for a function b in Lipschitz space Lip_α(R~n) with α∈(0,1),the commutator[b,V~(1/2)A~(-1/2)] is bounded from L_p(R~n) to L_q(R~n),where p,q∈(1,2] and 1/p-1/q =α/n.     

带参数的Littlewood-Paley g_λ~*函数的交换子在Morrey空间上的紧性

本文给出了交换子[b,g_λ~(*,ρ)]在Morrey空间L~(p,α)(R~n)上的紧性特征,其中1p∞,0αn.更精确地说,证明了交换子[b,g_λ~(*,ρ)]是Morrey空间上紧算子的充要条件是b∈VMO(R~n),其中g_λ~(*,ρ)表示带参数的Littlewood-Paley g_λ~*函数.     

一类Marcinkiewicz积分交换子的端点估计

本文得到Ω满足Dini型条件时,Marcinkiewicz积分交换子μΩ,b(f)的端点估计:|{x∈R~n:μΩ,b(f)(x)＞λ}|≤c‖b‖BMO∫_(R~n)(|f(x)|)/λ(1+log+(|f(x)|)/λ)dx．     

非齐型空间上分数型Marcinkiewicz积分算子的加权估计

令（X，d，μ）为满足所谓上倍双倍条件和几何双倍条件的度量测度空间.设M_β，ρ，q为（X，d，μ）上的分数型Marcinkiewicz积分算子.在本文中，作者证明了若β ∈[0，∞），ρ ∈（0，∞），q ∈（1，∞）且M_β，ρ，q在L²（μ）上有界，则M_β，ρ，q是从加权Lebesgue空间L^p（w）到加权弱Lebesgue空间L^p，∞（w）上有界和从加权Morrey空间L^p，κ，η（ω）到加权弱Morrey空间WL^p，κ，η（ω）上有界.     

反对角算子矩阵及其平方的(ω)性质的摄动

设H为复的无限维可分的Hilbert空间,B(H)为H上的有界线性算子的全体.若σ_a(T)\σ_(ea)(T)=π_(00)(T),则称T∈B(H)满足(ω)性质,其中σ_a(T)和σ_(ea)(T)分别表示算子T的逼近点谱和本质逼近点谱,π_(00)(T)={λ∈isoσ(T):0dimN(T-λI)∞}.T∈B(H)称为满足(ω)性质的摄动,若对任意的紧算子K,T+K满足(ω)性质.本文证明了反对角算子矩阵及其平方具有(ω)性质的摄动的等价性.     

素变量混合幂丢番图逼近

设λ_1,λ_2,λ_3,λ_4为不全为负的非零实数,λ_1/λ_2是无理数和代数数.■是具有良好间隔的序列,δ>0.本文证明了:对于任意ε>0及v∈■,v≤X,使得不等式|λ_1p_1~2+λ_2p_2~2+λ_3p_3~3+λ_4p_4~3-v|相似文献   

Jacobian-determinant equation in the critical Besov spaces

Let Ω be a bounded domain in R~n with smooth boundary. Here we consider the following Jacobian-determinant equation det u(x)=f(x),x∈Ω;u(x)=x,x∈?Ω where f is a function on Ω with min_Ω f = δ 0 and Ωf(x)dx = |Ω|. We prove that if f ∈B_(p1)~(np)(Ω) for some p∈(n,∞), then there exists a solution u ∈ B_(p1)~(np+1)(Ω)C~1(Ω) to this equation. On the other hand, we give a simple example such that u ∈ C_0~1(R~2, R~2) while detu does not lie in B_(p1)~(2p)(R~2) for any p∞.     

右半平面解析的Laplace-Stieltjes变换的广义级与型

给出右半平面解析的Laplace-Stieltjes变换的广义级与广义型的定义,研究了最大模M_u(σ,F)=sup{|∫_0~x e~(-(σ+it)y)dv(y)|:x∈(0,+∞),t∈R},最大项μ(σ,F)=max_(n∈N){A_n~*e~(-λnσ)},最大项指标v(σ,F)=max_k{λ_k|μ(σ,F)=A_k~*e~(-λkσ)}及其系数之间的关系,推广了Dirichlet级数的相关结果.     

幂次为2,3,4,5的素变量非线性型的整数部分

考虑了一个混合幂次为2,3,4,5的素变量非线性型的整数部分表示无穷多素数的问题.运用Davenport-Heilbronn方法证明了:如果λ_1,λ_2,λ_3,λ_4是正实数,至少有一个λ_i/λ_j(1≤ij≤4)是无理数,那么存在无穷多素数p_1,p_2,p_3,p_4,p,使得[λ_1p_1~2+λ_2p_2~3+λ_3p_3~4+λ_4p_4~5]=p.     

On Characterization of Poisson Integrals of Schrödinger Operators with Morrey Traces

Let L be a Schr?dinger operator of the form L =-Δ + V acting on L~2(R~n) where the nonnegative potential V belongs to the reverse H?lder class B_q for some q ≥ n. In this article we will show that a function f ∈ L~(2,λ)(R~n), 0 λ n, is the trace of the solution of L_u =-u_(tt) + L_u =0, u(x, 0) = f(x), where u satisfies a Carleson type condition sup x_B,r_Br_B~(-λ)∫_0~(rB)∫_(B(x_B,r_B))t|u(x,t)|~2dxdt≤C∞.Its proof heavily relies on investigate the intrinsic relationship between the classical Morrey spaces and the new Campanato spaces L_L~(2,λ)(R~n) associated to the operator L, i.e.L_L~(2,λ)(R~n)=L~(2,λ)(R~n).Conversely, this Carleson type condition characterizes all the L-harmonic functions whose traces belong to the space L~(2,λ)(R~n) for all 0 λ n.     

带多项式相位的高维振荡积分算子的有界性

考虑如下的振荡积分算子:T_(m,k,n)f(x):=∫_(R~n)e~(i(x_1~2+…+x_n~2))~m(y_1~2+…+y_n~2)~kf(y)dy,其中函数f为定义在R~n上的Schwartz函数,并且满足m,k0.本文给出算子T_(m,k,n).从L~p(R~n)(1≤p∞)到L~q(R~n)有界的一个充分必要条件.此外,我们还证明了算子T_(m,k,n)把L~1(R~n)映到C_0(R~n).     

Three Problems on Trigonometric Sums

Let Λ ? R~n be a uniformly discrete set and let C_Λ be the vector space consisting of all mean periodic functions whose spectrum is simple and contained in Λ. If Λ is a gentle set then for every f ∈ C_Λ we have f(x) = O(ω_Λ(x)) as |x| →∞ and ω_Λ(x) can be estimated(Theorem 4.1). This line of research was proposed by Jean-Pierre Kahane in 1957.