Riesz transforms for a non-symmetric Ornstein-Uhlenbeck semigroup

Let (ℋ _t ) _t≥0 be the Ornstein-Uhlenbeck semigroup on ℝ ^d with covariance matrix I and drift matrix −λ(I+R), where λ>0 and R is a skew-adjoint matrix and denote by γ _∞ the invariant measure for (ℋ _t ) _t≥0. Semigroups of this form are the basic building blocks of Ornstein-Uhlenbeck semigroups which are normal on L ²(γ _∞). We investigate the weak type 1 estimate of the Riesz transforms for (ℋ _t ) _t≥0. We prove that if the matrix R generates a one-parameter group of periodic rotations then the first order Riesz transforms are of weak type 1 with respect to the invariant measure γ _∞. We also prove that the Riesz transforms of any order associated to a general Ornstein-Uhlenbeck semigroup are bounded on L ^p (γ _∞) if 1<p<∞. The authors have received support by the Italian MIUR-PRIN 2005 project “Harmonic Analysis” and by the EU IHP 2002-2006 project “HARP”.     

Angle criteria for frame sequences and frames containing a Riesz basis

We obtain a condition implying that the union of two frame sequences is also a frame sequence. Christensen found a condition for this in terms of orthogonal projections. We phrase our condition by use of the angle between closed subspaces. Also a lower bound formula is obtained. We then apply the results to find conditions for a frame containing a Riesz basis to be a Riesz frame.     

Analyticity and Dynamic Behavior of a Damped Three-Layer Sandwich Beam

Using the Riesz basis approach, we study a sandwich beam that is composed of an outer stiff layer and a compliant middle layer. The dynamic behavior and analyticity of the system are obtained based on a detailed spectral analysis and Riesz basis generation. As a consequence, the analyticity of the solution and the exponential stability of the system are concluded. This work was supported by the National Natural Science Foundation of China, Program for New Century Excellent Talents in the Universities of China and by the National Research Foundation of South Africa.     

区域上Triebel-Lizorkin空间的分解

文中引进了区域上的Triebel-Lizorkin空间,以及原子和分子的概念,为了更好的理解这些空间,我们得到了这类Triebel-Lizorkin空间的原子分解和分子分解.这些结论是调和分析中函数空间分解理论的补充和完善.     

An unusual decomposition of a complete 7-partite graph of order 28

A decomposition of the complete 7-partite graph on 28 vertices where each set in the partition has four vertices is given. Several unusual properties of this decomposition are discussed, giving rise to several natural questions.     

锰族长竞选

Manganese has played an essential role in human life and production. Herein, this paper introduces the manganese's resources, properties and applications. Our aim is to make it easier for readers to understand in a more lively way.     

Quantitative analysis of organic additive content in a polymer by ToF-SIMS with PCA

Quantitative analysis of organic materials by ToF-SIMS is intrinsically difficult because of their tendency to decompose under ion irradiation. In this study, we applied principal component analysis (PCA) as a means of compensation for the spectral degradation caused by this decomposition and thus improve the accuracy of the quantitative analysis, using as models two organic additives of quite different composition and vulnerability to decomposition under ion irradiation, in polystyrene. This enables the extraction of a principal component related to their content that is independent of the decomposition. The effectiveness of this approach in quantitative analysis of organic additives content in polymers without loss in accuracy due to spectral degradation will be discussed.     

Necessary and Sufficient Conditions for the Boundedness of the Riesz Potential in Local Morrey-type Spaces

The problem of the boundedness of the Riesz potential I _α , 0 < α < n, in local Morrey-type spaces is reduced to the boundedness of the Hardy operator in weighted L _p -spaces on the cone of non-negative non-increasing functions. This allows obtaining sufficient conditions for the boundedness in local Morrey-type spaces for all admissible values of the parameters. Moreover, for a certain range of the parameters, these sufficient conditions coincide with the necessary ones. V. Guliyev’s research was partially supported by the grant of the Azerbaijan-U. S. Bilateral Grants Program II (project ANSF Award / AZM1-3110-BA-08) and the Turkish Scientific and Technological Research Council (TUBITAK, programme 2221, no. 220.01-619-4889).     

The Radon-Nikodým Property Does Not Imply the Separable Complementation Property

There is a Banach space X enjoying the Radon-Nikodým Property and a separable subspace Y which is not contained in any complemented separable subspace of X.     

On congruences and ideals of partially ordered quasigroups

Some results concerning congruence relations on partially ordered quasigroups (especially, Riesz quasigroups) and ideals of partially ordered loops are presented. These results generalize the assertions which were proved by Fuchs in [5] for partially ordered groups and Riesz groups.