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81.
Semyon B. Yakubovich 《Journal of Approximation Theory》2004,131(2):175
We establish analogs of the Hausdorff–Young and Riesz–Kolmogorov inequalities and the norm estimates for the Kontorovich–Lebedev transformation and the corresponding convolution. These classical inequalities are related to the norms of the Fourier convolution and the Hilbert transform in Lp spaces, 1p∞. Boundedness properties of the Kontorovich–Lebedev transform and its convolution operator are investigated. In certain cases the least values of the norm constants are evaluated. Finally, it is conjectured that the norm of the Kontorovich–Lebedev operator is equal to . It confirms, for instance, by the known Plancherel-type theorem for this transform when p=2. 相似文献
82.
The well-posedness of the Cauchy problem to the generalized Korteweg-de Vries-Benjamin-Ono equation is considered. Local results for data in (s?−1/8) and the global well-posedness for data in are obtained if l=2. Moreover, for l=3, the problem is locally well-posed for data in Hs (s?1/4). The main idea is to use the Fourier restriction norm method. 相似文献
83.
Two-Parametric Compound Binomial Approximations 总被引:1,自引:0,他引:1
We consider two-parametric compound binomial approximation of the generalized Poisson binomial distribution. We show that the accuracy of approximation essentially depends on the symmetry or shifting of distributions and construct asymptotic expansions. For the proofs, we combine the properties of norms with the results for convolutions of symmetric and shifted distributions. In the lattice case, we use the characteristic function method. In the case of almost binomial approximation, we apply Steins method.__________Published in Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 443–466, October–December, 2004. 相似文献
84.
Let be a nonempty closed convex subset of a real Banach space and be a Lipschitz pseudocontractive self-map of with . An iterative sequence is constructed for which as . If, in addition, is assumed to be bounded, this conclusion still holds without the requirement that Moreover, if, in addition, has a uniformly Gâteaux differentiable norm and is such that every closed bounded convex subset of has the fixed point property for nonexpansive self-mappings, then the sequence converges strongly to a fixed point of . Our iteration method is of independent interest.
85.
Shutao Chen Yunan Cui Henryk Hudzik 《Proceedings of the American Mathematical Society》2004,132(2):473-480
Criteria in order that an Orlicz space equipped with the Orlicz norm contains a linearly isometric copy (or an order linearly isometric copy) of (or ) are given.
86.
It will be shown that a normed partially ordered vector space is linearly, norm, and order isomorphic to a subspace of a normed Riesz space if and only if its positive cone is closed and its norm p satisfies p(x)p(y) for all x and y with -yxy. A similar characterization of the subspaces of M-normed Riesz spaces is given. With aid of the first characterization, Krein's lemma on directedness of norm dual spaces can be directly derived from the result for normed Riesz spaces. Further properties of the norms ensuing from the characterization theorem are investigated. Also a generalization of the notion of Riesz norm is studied as an analogue of the r-norm from the theory of spaces of operators. Both classes of norms are used to extend results on spaces of operators between normed Riesz spaces to a setting with partially ordered vector spaces. Finally, a partial characterization of the subspaces of Riesz spaces with Riesz seminorms is given. 相似文献
87.
Abstract
In this paper, we establish the relationship between
Hausdorff measures and Bessel capacities on any nilpotent
stratified Lie group
(i. e., Carnot group). In particular, as a special corollary of
our much more general results, we have the following theorem
(see Theorems A and E in Section 1):
Let Q be the
homogeneous dimension of
.
Given any set E ⊂
,
B
α,p
(E) = 0 implies ℋ
Q−αp+ ε(E) = 0 for all ε > 0. On the other
hand, ℋ
Q−αp
(E) < ∞ implies
B
α,p
(E) = 0. Consequently, given any set
E ⊂
of Hausdorff dimension Q −
d, where 0 <
d <
Q, B
α,p
(E) = 0 holds if and only if αp ≤ d.
A version of O. Frostman’s theorem concerning Hausdorff
measures on any homogeneous space is also established using the
dyadic decomposition on such a space (see Theorem 4.4 in Section
4).
Research supported partly by the U. S. National
Science Foundation Grant No. DMS99–70352 相似文献
88.
Let X and Y be Banach spaces and ψ a continuous convex function on the unit interval [0,1] satisfying certain conditions. Let X⊕ψY be the direct sum of X and Y equipped with the associated norm with ψ. We show that X⊕ψY is uniformly convex if and only if X,Y are uniformly convex and ψ is strictly convex. As a corollary we obtain that the ?p,q-direct sum (not p=q=1 nor ∞), is uniformly convex if and only if X,Y are, where ?p,q is the Lorentz sequence space. These results extend the well-known fact for the ?p-sum . Some other examples are also presented. 相似文献
89.
J. Extremera 《Journal of Functional Analysis》2003,197(1):212-227
Let G be a compact group. If the trivial representation of G is not weakly contained in the left regular representation of G on L02(G) and X is either Lp(G) for 1<p?∞ or C(G), then we show that every complete norm |·| on X that makes translations from (X,|·|) into itself continuous is equivalent to ||·||p or ||·||∞ respectively. If 1<p?∞ and every left invariant linear functional on Lp(G) is a constant multiple of the Haar integral, then we show that every complete norm |·| on Lp(G) that makes translations from (Lp(G),|·|) into itself continuous and that makes the map t?Lt from G into bounded is equivalent to ||·||p. 相似文献
90.
In this paper, theoretical results are described on the maximum norm stability and accuracy of finite difference discretizations of parabolic equations on overset nonmatching space-time grids. We consider parabolic equations containing a linear reaction term on a space-time domain which is decomposed into an overlapping collection of cylindrical subregions of the form , for . Each of the space-time domains are assumed to be independently grided (in parallel) according to the local geometry and space-time regularity of the solution, yielding space-time grids with mesh parameters and . In particular, the different space-time grids need not match on the regions of overlap, and the time steps can differ from one grid to the next. We discretize the parabolic equation on each local grid by employing an explicit or implicit -scheme in time and a finite difference scheme in space satisfying a discrete maximum principle. The local discretizations are coupled together, without the use of Lagrange multipliers, by requiring the boundary values on each space-time grid to match a suitable interpolation of the solution on adjacent grids. The resulting global discretization yields a large system of coupled equations which can be solved by a parallel Schwarz iterative procedure requiring some communication between adjacent subregions. Our analysis employs a contraction mapping argument.
Applications of the results are briefly indicated for reaction-diffusion equations with contractive terms and heterogeneous hyperbolic-parabolic approximations of parabolic equations.