Vilenkin群上的加权Hardy空间中的乘子

本文主要研究了Vilenkin群上的加权Hardy空间的原子分解,证明了一个加权H^p乘子定理并给出其应用。     

Potential Operators in Weighted Herz-Type Spaces over Locally Compact Vilenkin Groups

Let G be a bounded locally compact Vilenkin group. We study the boundedness of potential operators and the maximal operators associated with them in the weighted Herz space, the weighted Hardy space and the weighted Herz-type Hardy space over G. We also discuss the boundedness of these operators on the weighted weak Lebesgue space and the weighted weak Herz space whose sharpness are also discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

局部紧Vilenkin群上Herz空间的一个分解定理

In this paper, by applying a vector-valued inequality we obtained a decomposition theorem on Herz spaces over locally compact Vilenkin groups with new range 0 < q≤1.     

Structure Properties and Real Continuous Bounded 2-Cohomology of Locally Compact Groups

With the help of some structure results for locally compact groups, the second real continuous bounded cohomology group of a connected locally compact group is described and it is proved that the corresponding group is finite-dimensional for any almost connected locally compact group.     

Geometrizing Infinite Dimensional Locally Compact Groups

We study groups having invariant metrics of curvature bounded below in the sense of Alexandrov. Such groups are a generalization of Lie groups with invariant Riemannian metrics, but form a much larger class. We prove that every locally compact, arcwise connected, first countable group has such a metric. These groups may not be (even infinite dimensional) manifolds. We show a number of relationships between the algebraic and geometric structures of groups equipped with such metrics. Many results do not require local compactness.

     

局部紧Vilenkin群上弱Morrey-Herz空间中一些算子的有界性

首先引入了一个新空间—局部紧Vilenkin群G上弱齐次Morrey-Herz空间WMK_(p,q)~(α,λ)(G),然后在WMK_(p,q)~(α,λ)(G)上讨论了一些奇异积分算子和分数次奇异积分算子的有界性问题.     

Induced Corepresentations of Locally Compact Quantum Groups

We introduce the construction of induced corepresentations in the setting of locally compact quantum groups and prove that the resulting induced corepresentations are unitary under some mild integrability condition. We also establish a quantum analogue of the classical bijective correspondence between quasi-invariant measures and certain measures on the larger locally compact group.     

Locally Compact Topological Groups and Cofinal Completeness

It is proved that a Tychonoff topological group is locally compactif and only if it is of pointwise countable type and its leftuniformity is cofinally complete. From this result a characterizationis derived of those T₀ paratopological groups (X, ) of pointwisecountable type for which (X, ^–1) is locally compactand also a characterization is deduced of locally pseudocompacttopological groups in terms of cofinal completeness. Also characterizedare the Tychonoff topological groups of pointwise countabletype for which their left uniformity has property U. Finally,cofinal completeness of the Hausdorff–Bourbaki uniformityof a topological group is studied.     

Totally Disconnected and Locally Compact Heisenberg-Weyl Groups

Harmonic analysis on ℤ(p ^ℓ ) and the corresponding representation of the Heisenberg-Weyl group HW[ℤ(p ^ℓ ),ℤ(p ^ℓ ),ℤ(p ^ℓ )], is studied. It is shown that the HW[ℤ(p ^ℓ ),ℤ(p ^ℓ ),ℤ(p ^ℓ )] with a homomorphism between them, form an inverse system which has as inverse limit the profinite representation of the Heisenberg-Weyl group \mathfrak HW[\mathbbZ_p,\mathbbZ_p,\mathbbZ_p]\mathfrak {HW}[{\mathbb{Z}}_{p},{\mathbb{Z}}_{p},{\mathbb{Z}}_{p}]. Harmonic analysis on ℤ _p is also studied. The corresponding representation of the Heisenberg-Weyl group HW[(ℚ _p /ℤ _p ),ℤ _p ,(ℚ _p /ℤ _p )] is a totally disconnected and locally compact topological group.     

Generalized Group Algebras of Locally Compact Groups

This article studies the homological properties of generalized group algebra L ¹(G, A) of a locally compact group G over a Banach algebra A with an identity of norm 1. It is shown that if L ¹(G, A) is right continuous then G is finite and A is right continuous. It is also shown that L ¹(G, A) is right self-injective if and only if G is finite and A is right self-injective.     

On the One Sided Translates of Powers of Continuous Functions on Locally Compact Groups

We prove that the one sided translates of powers of a real valued continuous (respectively compactly supported) function with a unique maximum (or minimum) span a dense subspace in C(G) and C(X) (respectively in L ^P (G) and L ^P (X)) for any locally compact group G and for any Riemannian symmetric space X.     

Boundedness of Some Singular Integral Operators on Morrey-Herz Spaces over Locally Compact Vilenkin Groups

In this paper the boundedness results for some fractional and singular integral operators on the homogeneous Morrey-Herz spaces over locally compact Vilenkin groups are shown.     

Continuous Selections and Locally Pseudocompact Groups

We characterize locally pseudocompact groups by means of the selection theory. Our result is the selection version of the well-known Comfort—Ross theorem on pseudocompactness which states that a topological group is pseudocompact if and only its Stone—Čech compactification is a topological group.     

Littlewood–Paley and Multiplier Theorems on Weighted Spaces over Locally Compact Vilenkin Groups

We extend the Littlewood–Paley theorem toL^p_w(G), whereGis a locally compact Vilenkin group andware weights satisfying the MuckenhouptA_pcondition. As an application we obtain a mixed-norm type multiplier result onL^p_w(G) and prove the sharpness of our result. We also obtain a sufficient condition for φ L^∞(Γ) to be a multiplier on the power weightedL^p_α(G) in terms of its smoothness condition.     

Abstract Coherent State Transforms Over Homogeneous Spaces of Compact Groups

This paper presents theoretical aspects of a unified generalization for the abstract theory of coherent state/voice transforms over homogeneous spaces of compact groups using operator theory. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and \(\mu \) be the normalized G-invariant measure on G/H associated to the Weil’s formula with respect to the probability measures of G, H. Let \((\pi ,\mathcal {H}_\pi )\) be a continuous unitary representation of G with non-zero mean over H. In this article, we introduce the generalized notion of coherent state/voice transform associated to \(\pi \) on the Hilbert function \(L^2(G/H,\mu )\). We then study basic analytic properties of these transforms.     

Fundamental Sets of Functions on Locally Compact Abelian Groups

Let G be a locally compact Abelian group, and let X be a compact set of G. Given a positive definite function ?: G × G → ? whose real part is continuous at neutral element of G, we research a necessary and sufficient setting for the linear span of the set {x ∈ X → ?(x ? y): y ∈ X} to be dense in C(X) in the topology of uniform convergence. The context treated that is abstract encompasses classical cases of the literature, while other examples are entirely new.