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研究一类带Hardy-Sobolev临界指数的Kirchhoff型方程其中Ω⊂R3是一个有界开区域且边界∂Ω光滑，0∈Ω，a，b≥0且a+b>0，λ>0，0 < q < 1，0≤s<1。利用变分方法，获得该问题正解的存在性结果。
Despite a true antipathy to the subject Hardy contributed deeply to modern probability. His work with Ramanujan begat probabilistic number theory. His work on Tauberian theorems and divergent series h...
Restrictions to Invariant Subspaces of Composition Operators on the Hardy Space of the Disk
composition operator hardy semigroup
2015/1/19
Invariant subspaces are a natural topic in linear algebra and operator theory. In some rare cases, the restrictions of operators to different invariant subspaces are unitarily equivalent, such as cert...
Commutants of composition operators on the Hardy space of the disk
Composition operator Commutant Hardy space
2015/1/19
The main part of this thesis, Chapter 4, contains results on the commutant of a semigroup of operators defined on the Hardy Space of the disk where the operators have hyperbolic non-automorphic symbol...
带Hardy项的半线性椭圆方程非球对称解的研究（图）
非球对称解 变分方法 能量极小解 分支理论
2013/10/17
非球对称解的存在性.这里Ω={x|x∈Rn,n≥3,a<|x|<1} 是 Rn (n≥3) 中的环,其中0≤μ< μ=((n-2)/2})2,f(u)为已知函数.本文在讨论球对称解的性质的基础上,利用变分方法得到了方程的极小能量解的存在性,并且利用分支理论得到了方程的非球对称解.
Optimal relations between Lp-norms for the Hardy operator and its dual
Hardy operator Dual operator Best constants
2012/6/29
We obtain sharp two-sided inequalities between $L^p-$norms $(1Hardy operator, $H^*$ is its dual, and $f$ is a nonnegative measurable function...
Estimates for approximation numbers of some classes of composition operators on the Hardy space
approximation numbers Blaschke product composition operator cusp map Hardy space modulus of continuity Schatten classes
2012/6/21
We give estimates for the approximation numbers of composition operators on $H^2$, in terms of some modulus of continuity. For symbols whose image is contained in a polygon, we get that these approxim...
Valuation theory of exponential Hardy fields
Valuation theory of exponential Hardy fields Logic
2012/6/19
We describe the residue fields of arbitrary convex valuations on certain o-minimal expansions of the ordered field of real numbers. References: [1] Franz-Viktor and Salma Kuhlmann: Residue fields of a...
A Cesaro Average of Hardy-Littlewood numbers
Goldbach-type theorems Hardy-Littlewood numbers Laplace transforms Cesaro averages
2012/6/14
Let $\Lambda$ be the von Mangoldt function and (r_{\textit{HL}}(n) = \sum_{m_1 + m_2^2 = n} \Lambda(m_1),) be the counting function for the Hardy-Littlewood numbers. Let $N$ be a sufficiently large in...
Polyharmonic Hardy Spaces on the Complexified Annulus and Error Estimates of Cubature Formulas
Hardy space Numerical Integration Cubature formulas Error estimate
2012/4/23
The present paper has a twofold contribution: first, we introduce a new concept of Hardy spaces on a multidimensional complexified annular domain which is closely related to the annulus of the Klein-D...
A heat kernel version of Hardy's theorem for the Laguerre hypergroup
Laguerre hypergroup Uncertainty principle Hardy's theorem
2011/9/30
The uncertainty principle says that a function and its Fourier transform can't simultaneously decay very rapidly at infinity. A classical version of uncertainty principle, known as Hardy's theorem, wa...
A heat kernel version of Hardy's theorem for the Laguerre hypergroup
Laguerre hypergroup Uncertainty principle Hardy's theorem
2011/9/29
The uncertainty principle says that a function and its Fourier transform can't simultaneously decay very rapidly at infinity. A classical version of uncertainty principle, known as Hardy's theorem, wa...
Hardy Spaces $H_L^p({\mathbb R}^n)$ Associated to Operators Satisfying $k$-Davies-Gaffney Estimates
Hardy space Hardy-Sobolev space k-Davies-Gaffney estimate Schrodinger type operator
2011/9/21
Abstract: Let $L$ be a one to one operator of type $\omega$ having a bounded $H_\infty$ functional calculus and satisfying the $k$-Davies-Gaffney estimates with $k\in{\mathbb N}$. In this paper, the a...
Endpoint Boundedness of Riesz Transforms on Hardy Spaces Associated with Operators
Riesz transform Davies-Gaffney estimate Schrodinger operator second order elliptic operator Hardy space
2011/9/21
Abstract: Let $L_1$ be a nonnegative self-adjoint operator in $L^2({\mathbb R}^n)$ satisfying the Davies-Gaffney estimates and $L_2$ a second order divergence form elliptic operator with complex bound...
Some new Inequalities of Hardy-Hilbert Type with general kernel
Hardy-Hilbert’s inequality Hardy’s inequalities Holder inequality
2011/9/20
Abstract: In this paper, by using hardy inequality, we establish some new integral inequalities of Hardy-Hilbert type with general kernel. As applications, equivalent forms and some particular results...