查询词典 Hardy

Brown and Halmos [3] showed that the only compact Toeplitz operator on the Hardy space is the zero operator and a Toeplitz operator is bounded on the Hardy space if and only if its symbol is bounded.

Brown和Halmos[3]证明了经典Hardy空间上只有零算子才是紧的Toeplitz算子，并且证明了Toeplitz算子有界等价于它的符号是有界的。

In the six chapter, we use the methods of reproducing kernel and Carleson measure charactering the pointwise multipliers on the Hardy space, Bergman space on the polydiscs, we also obtain a necessary condition for a composition operator to be a compact operator, and a addition result on the range of composition operator on the Hardy space.

在第六章中，我们利用再生核与Carl e Son测度刻画了多圆Hardy空间到Bergman空间，以及Bergman空间到Bergman空间的点乘子，得到Hardy空间与Bergman空间上复合算子为紧的一个必要条件，以及在Hardy空间上关于复合算子值域的一个结果。

ChinaWang Yonghuidirected by Zhang ~Venpeng The main purpose of thesis is using the mean value theorem of the Dirichlet Lunctions to study the asymptotic property of the Dedekind sums and Hardy sums, and give two sharper asymptotic formulas.

关于Dedekind和的推广型均值公式及Hardy和的推广型均值公式本论文利用Dirichlet L-函数的均值定理研究了Dedekind和及Hardy和的一类均值估计问题，并给出了较为精确的渐近公式。

We proved that this kind of operators were bounded from Hardy space to Lebesgue space, and they were bounded operators on the Hardy space if they satisfied some special conditions.

利用Hardy空间和Herz型Hardy空间的原子和分子分解特征，文中首先给出了此类算子从Hardy空间到Lebesgue空间上的有界性，而且，在满足一定的消失矩时，它又是Hardy空间上的有界算子。

In chapter 3,we investigate the boundedness of multilinear commutators of singular integral operators and fractional integral operators with Lipschitz functions on the Hardy-type spaces.

本章我们得到了和在L~p，Hardy型空间H_~p和Herz型Hardy空间H_q，

A discrete weighted Hardy inequality is studied, and by proving a refinement lemma, the characterization of the weight sequence ｛ω_｝_(n≥1) in order that the weighted l~-Hardy inequality holds for all nonnegative and nonincreasing sequence c_ is given.

本文研究离散的加权Hardy不等式，通过建立权序列的加细引理，给出了对任何非负非增数列 lp-加权Hardy不等式成立时权序列{ωn}n≥1的特征刻划。

Along with the developing of the molecole characterization of the weighted Herz type Hardy space, the study of the singular integral operator get a plentiful harvest.

本文首先解决了加权Herz型Hardy空间的分子刻画，作为应用，给出了强奇异积分算子T_b在加权Herz型Hardy空间上的有界性的证明。

In the fourth chapter,we discuss theapplication of the atomic decomposition theory to the vector-valued harmonicanalysis.We give the Hardy inequalities in the vector-valued martingale space,we also study the Mikhlin multiplier operator and singular integral operator in thevector-valued Hardy space.

第四章我们主要研究原子分解理论在向量值调和分析中的应用，建立了向量值鞅空间上的Hardy不等式，向量值Hardy空间上的Mikhlin乘子算子及一类奇异积分算子的有界性。

His simple and elegant 1930 proof of the Hardy–Littlewood theorem found its place in the well-known monographs by Titchmarsh, Knopp, Doetsch, Widder, Hardy and Favard.

他简单而优雅的1930年证明了的Hardy - Littlewood定理发现它由蒂施马奇，诺普，Doetsch担任，万邦，哈代和Favard著名的专着的地方。

Recently,atoms with higher order vanishing moment were defined by Krant-z etc on some particular spaces of homogeneous type,but it hasn't been solvedthoroughly on usual spaces of homogeneous type.On the other hand,krantz'sstudy was made under the condition which the measure of the sets constructedby single element is zero,therefore their work didn't include the case of integ-er Z as a particular space of homogeneous type.Indeed,as a Hardy space on Z,〓(0＜p≤1)has been studied by some scholars.

尽管近来Krantz等人在某些齐型空间上定义了带高阶消失矩的原子，但在一般的齐型空间上建立带高阶消失矩的原子Hardy空间还没有完全解决，而且Krantz等人的工作是在单点集测度为零的条件下讨论的，因而不包括作为齐型空间的整数Z的情形。Z作为一类特殊的齐型空间，其上Hardy空间〓的问题有不少学者讨论过。

It is also known as one of the most poisonous naturally occurring substances.

它也被称为一个最自然发生的有毒物质。

The greatest stress is found at the location on the cross section where V is the largest.

最大应力出现在横截面上V为最大的地方。