粗糙核多线性分数次积分算子在加权Herz空间的有界性

研究两类带粗糙核的多线性分数次积分算子T_(Ω,α)~A, T_(Ω,α)~Af(x)=∫R_m(A;x,y)/R~n|x- y|~(n+m-α-1)Ω(x-y)f(y)dy及其相关的极大算子M_(Ω,α)~A在加权Herz空间的有界性,其中Ω∈L~s(S~(n-1))(s>1)是R~n中的零次齐次函数,m∈N,A有m=1阶导数且D~γA∈BMO(R~n)或D~γA∈L~r(R~n)(|γ|=m -1,1相似文献   

带变量核的分数次积分算子在Herz型Hardy空间上的有界性

正1引言令S~(n-1)(n≥2)是R~n中的单位球面,dσ是S~(n-1)上规范的Lebesgue测度,且定义在R~n×R~n上的函数为Ω(x,z).若Ω(x,z)满足如下两条件:(1)Ω(x,λz)=Ω(x,z),对于任意的x,z∈R~n,及λ0;     

Marcinkiewicz积分交换子的加权有界性(英文)

本文应用加权Hardy空间H_ω~p(R~n)上的原子分解理论,研究了由函数b∈Λβ(R~n)(0<β≤1)与Marcinkiewicz积分μ_Ω生成的交换子μ_Ω~b的有界性;证明了μ_Ω~b是从L~q(ω~q)到L~q(ω~q)有界的,从L~1(|x|γ(n-β)/n)到弱L(n/n-β)(|x|~γ)有界的,且从H~p(ω~p)到L~q(ω~q)有界的,这里1/p-1/q=β/n.     

Marcinkiewicz积分交换子在一些Hardy空间的有界性

讨论了由核函数满足具有某类Dini条件的Marcinkiewicz积分μΩ及函数b∈Lipβ(R~n)生成的交换子μ(_Ω,b)~m的性质.证明了Marcinkiewicz积分交换子μ_(_Ω,b)~m在Hardy型空间H_(bm,s)(R~n)上有界,也在Herz型Hardy空间H_(bm)K_p~(a_q)(R~n)上有界.     

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.     

广义Campanato空间上粗糙核参数型Marcinkiewicz积分

作为一类Littlewood-Paley函数,μ_(Ω,b)~ρ(f)是带非齐次粗糙核的参数型Marcinkiewicz积分,其中粗糙核Ω∈L~q(S~(n-1))满足消失性和积分Dini连续,径向核b∈Δ_s(R~+)∩Θ_s(R~n),1q,s∞,复参数ρ具有正实部.仅在一点有限的假设下,该文建立了μ_(Ω,b)~ρ(f)在广义Campanato空间L~(p,φ)(R~n)上的存在性和有界性,本质地推进了众多的已有工作.     

具临界指数的非线性椭圆方程多重解的存在性

于此α=±1,ΩR~n是具光滑边界的有界区域,τ=(n 2)/(n-2)是Sololev临界指数。 近年来,H.Brezis和L.Nirenberg证明了当α=1,n≥4且0<λ<λ_1时,问题(Ⅰ)至少有一个正解.于此λ_1是—Δ的第一特征值。嗣后,A.Capozzi,D.Fortunato和G.Palmieri证明,对任何λ>0,问题(Ⅰ)至少有一对非零解。     

解广义特征值反问题的同伦方法

1.引言 我们讨论下列广义特征值反问题: (G)已知B是n×n阶对称半正定矩阵,λ=(λ_1,…,λ_(2n-1))~T∈R~(2n-1),且{λ_i}~(n_3),和{λ_i}_(n+1)~(2n-1)严格交错。问题是欲求一个实对称三对角n×n阶矩阵A,使得λ_1…,λ_n是Ax=λBx的特征值,λ_(n+1),…,λ_(2n-1)是A_(n-1)x=λB_(n-1)x的特征值,其中A_(n-1),B_(n-1)分别是矩阵A,B的前n-1阶主子阵。     

双曲域上的对数导数与Bloch函数

设Ω是有限复平面C上的双曲型区域,λ_Ω(z)|dz|是其上的双曲度量;置δ_Ω(z)=dist(z,Ω),[1/δ_Ω(z)]|dz|称为Ω上的拟双曲度量.又记Ω上的Bloch函数全体为B(Ω).本文引进了Ω上的对数可导函数空间T(Ω)和拟对数可导函数空间QT(Ω),并讨论了它们的一些性质.对数导函数区别λ_Ω(z)与1/δ_Ω(z),以及此时候T(Ω)的几何特征;T(Ω)与B(Ω)之间的关系;QT(Ω)的渐近特征.     

一类广义的Marcinkiewicz积分算子的有界性

研究了下述广义Marcinkiewicz积分算子μΩ,αf(x)=∫∞0|∫|x-y|≤tΩ(x-y)|x-y|n-1f(y)dy|2dtt3+2α12当零次齐次函数Ω∈Hq(Sn-1),q=n-1n-1+α,α≥0,且满足一定的消失性,则对于任意的1相似文献   

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Singularities of Solutions of One Class of Equations of Continuum Mechanics

We analyze one class of families of integral equations and describe the dependence of the singularities of solutions of integral equations on the dimensions of the families of kernels of equations. On the basis of these results, we propose procedures for the construction of approximate solutions for a small parameter.     

Determination of asymptotic solutions of problems of nonlinear theories of thermoviscoelasticity

It is shown that the asymptotic solution of a problem of the nonlinear theory of thermoviscoelasticity, if it exists, can be found directly from the solution of the asymptotic boundary-value problem without completely solving the starting problem.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 3, pp. 395–400, May–June, 1976.     

Emptiness of set of points of lower semicontinuity of Lyapunov exponents

We consider parametric families of differential systems with coefficients that are bounded and continuous on the half-line and uniformly in time continuously depend on a real parameter. For each Lyapunov exponent, we construct a family such that the Lyapunov exponent of its systems treated as a function of the parameter is not a lower semicontinuous function for any value of the parameter.     

图表示范畴的两个子范畴

引进图表示范畴的两个子范畴,研究它们的同调性质。