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991.
Littlewood-Paley算子交换子在加权Herz型Hardy空间上的有界性 总被引:2,自引:1,他引:1
研究了Littlewood-Paley算子交换子gψ,b在加权Herz型Hardy空间上的性质,并证明了gψ,b在某些条件下是HKa,pq(ω1,ω2)到Ka,pq(ω1,ω2)和HKa,pq(ω1,ω2)到WKa,pq(ω1,ω2)上的有界算子. 相似文献
992.
通过放宽尺寸条件,得到了一类具有分数次积分性质的次线性算子从Herz型Hardy空间到(弱)Herz型Hardy空间有界性的判定条件,以及端点处的弱型估计. 相似文献
993.
Mitsuru Sugimoto Naohito Tomita 《Proceedings of the American Mathematical Society》2008,136(5):1681-1690
We prove that pseudo-differential operators with symbols in the class ( ) are not always bounded on the modulation space ().
994.
Sharp constants are exhibited in exponential inequalities corresponding to the limiting case of the Sobolev inequalities in
Lorentz-Sobolev spaces of arbitrary order.
相似文献
995.
Martin Sleziak 《Applied Categorical Structures》2008,16(4):451-478
Hereditary coreflective subcategories of an epireflective subcategory A of Top such that I 2 ? A (here I 2 is the two-point indiscrete space) were studied in [4]. It was shown that a coreflective subcategory B of A is hereditary (closed under the formation subspaces) if and only if it is closed under the formation of prime factors. The main problem studied in this paper is the question whether this claim remains true if we study the (more general) subcategories of A which are closed under topological sums and quotients in A instead of the coreflective subcategories of A. We show that this is true if A ? Haus or under some reasonable conditions on B. E.g., this holds if B contains either a prime space, or a space which is not locally connected, or a totally disconnected space or a non-discrete Hausdorff space. We touch also other questions related to such subclasses of A. We introduce a method extending the results from the case of non-bireflective subcategories (which was studied in [4]) to arbitrary epireflective subcategories of Top. We also prove some new facts about the lattice of coreflective subcategories of Top and ZD. 相似文献
996.
K. L. Avetisyan 《Potential Analysis》2008,29(1):49-63
We study anisotropic mixed norm spaces h(p,q,α) consisting of n-harmonic functions on the unit polydisc of by means of fractional integro-differentiation including small 0 < p < 1 and multi-indices α = (α
1,...,α
n
) with non-positive α
j
≤ 0. As an application, two different Bloch spaces of n-harmonic functions are characterized.
相似文献
997.
Philippe Clement Wolfgang Desch 《Proceedings of the American Mathematical Society》2008,136(1):333-339
We give an elementary proof for the triangle inequality of the -Wasserstein metric for probability measures on separable metric spaces. Unlike known approaches, our proof does not rely on the disintegration theorem in its full generality; therefore the additional assumption that the underlying space is Radon can be omitted. We also supply a proof, not depending on disintegration, that the Wasserstein metric is complete on Polish spaces.
998.
Ihab Al Alam 《Proceedings of the American Mathematical Society》2008,136(1):193-201
in . In the present paper, we prove that there is a Müntz space not complemented in .
999.
Learning function relations or understanding structures of data lying in manifolds embedded in huge dimensional Euclidean
spaces is an important topic in learning theory. In this paper we study the approximation and learning by Gaussians of functions
defined on a d-dimensional connected compact C
∞ Riemannian submanifold of which is isometrically embedded. We show that the convolution with the Gaussian kernel with variance σ provides the uniform approximation order of O(σ
s
) when the approximated function is Lipschitz s ∈(0, 1]. The uniform normal neighborhoods of a compact Riemannian manifold play a central role in deriving the approximation
order. This approximation result is used to investigate the regression learning algorithm generated by the multi-kernel least
square regularization scheme associated with Gaussian kernels with flexible variances. When the regression function is Lipschitz
s, our learning rate is (log2
m)/m)
s/(8 s + 4 d) where m is the sample size. When the manifold dimension d is smaller than the dimension n of the underlying Euclidean space, this rate is much faster compared with those in the literature. By comparing approximation
orders, we also show the essential difference between approximation schemes with flexible variances and those with a single
variance.
Supported partially by the Research Grants Council of Hong Kong [Project No. CityU 103405], City University of Hong Kong [Project
No. 7001983], National Science Fund for Distinguished Young Scholars of China [Project No. 10529101], and National Basic Research
Program of China [Project No. 973-2006CB303102]. 相似文献
1000.
Dorina Mitrea 《Transactions of the American Mathematical Society》2008,360(7):3771-3793
Let be the solution operator for in , Tr on , where is a bounded domain in . B. E. J. Dahlberg proved that for a bounded Lipschitz domain maps boundedly into weak- and that there exists such that is bounded for . In this paper, we generalize this result by addressing two aspects. First we are also able to treat the solution operator corresponding to Neumann boundary conditions and, second, we prove mapping properties for these operators acting on Sobolev (rather than Lebesgue) spaces.