Addendum to: Comparison between different types of abstract integrals in riesz spaces

In [3] we did not give explicitly the definition of measurability for realvalued functions, with respect to finitely additive measures with values in a Dedekind complete Riesz space. We note that, in [3], all involved functions are intended to be measurable. We now report the definition of measurability, which we gave in [2] (Definition 3.2). Lavoro svolto nell’ ambito dello G.N.A.F.A. del C.N.R.     

Comparison between different types of abstract integrals in Riesz spaces

A comparison among different types of integral in Riesz spaces is given.     

Addendum to: large deviations asymptotics for spherical integrals

We correct an omission in Guionnet and Zeitouni (J. Funct. Anal. 188 (2002) 461) and improve the main result there to a full-large deviations trajectorial result.     

Differentiation in abstract spaces

A new definition of differentiation for mappings between topological vector spaces is introduced. It does not require the mapping to be defined on a linear manifold, nor does it require it to be continuous. All of the main theorems of differential calculus hold and all other known definitions of differentiation are included. The new definition can be used for singular mappings and those defined on arbitrary sets. Applications are given.     

Applications of operator spaces to abstract harmonic analysis

We give a survey of how the relatively young theory of operator spaces has led to a deeper understanding of the Fourier algebra of a locally compact group (and of related algebras).     

Applications of some block spaces to singular integrals

This paper is a survey on the theory and application of some block spaces on the unit sphere introduced by Jiang and the author of this paper in the study of singular integrals and some related operators with rough kernels.      

Almost everywhere convergence of riesz means on certain noncompact symmetric spaces

Summary Let G/K be a rank one or complex non compact symmetric space of dimension l. We prove that if f L^p, 1p2, the Riesz means of order z of f with respect to the eigenfunction expansion of the Laplacian converge to falmost everywhere for Re(z)>(l, p). The critical index (l, p) is the same as in the classical result of Stein in the Euclidean case.The first author was supported by funds of the Ministero della Pubblica Istruzione. The work was done while the second author was a member of the Mathematical Sciences Research Institute at Berkeley, with a fellowship from the Consiglio Nazionale delle Ricerehe.     

Asymptotic kuhn-tucker conditions in abstract spaces

Asymptotic extensions of the Kuhn-Tucker conditions, in which both the adjoint equation and the complementary slackness condition are solved asymptotically, are given for vector-valued mathematical programming problems in locally convex spaces. Under appropriate hypotheses, the conditions are both necessary and sufficient for optimality. In particular, they characterize optimality for linear programs. An asymptotic dual program is also given.     

一类粗糙核参数型Marcinkiewicz积分

In this paper,the L2-boundedness of a class of parametric Marcinkiewicz integral μρΩ,h with kernel function Ω in Bq0.0 (Sn-1) for some q＞ 1,and the radial function h (x)∈ l∞ (Ls) (R+) for 1＜s≤∞ are given. The Lp(Rn) (2≤p＜∞) boundedness of μ*Ω,ph,λ and μρΩ,h,s with Ω in Bq0,0(Sn-1) and h(|x|)∈l∞(Ls)(R+) in application are obtained. Here μ*Ω,p h,λ and μpΩ,h,s are parametric Marcinkiewicz integrals corresponding to the Littlewood-Paley gλ* function and the Lusin area function S,respectively.     

Anisotropic singular integrals in product spaces

In this paper, the authors introduce a class of product anisotropic singular integral operators, whose kernels are adapted to the action of a pair A := (A1, A2) of expansive dilations on R n and R m , respectively. This class is a generalization of product singular integrals with convolution kernels introduced in the isotropic setting by Fefferman and Stein. The authors establish the boundedness of these operators in weighted Lebesgue and Hardy spaces with weights in product A∞ Muckenhoupt weights on R n × R m . These results are new even in the unweighted setting for product anisotropic Hardy spaces.     

Bochner integrals in ordered vector spaces

We present a natural way to cover an Archimedean directed ordered vector space E by Banach spaces and extend the notion of Bochner integrability to functions with values in E. The resulting set of integrable functions is an Archimedean directed ordered vector space and the integral is an order preserving map.     

A NOTE TO OSCILLATORY SINGULAR INTEGRALS ON HERZ—TYPE SPACES

In this paper, we want to improve our previous results. We prove that some oscillatory strong singular integral operators of non-convolution type with non-polynomial phases are bounded from Herz-type Hardy spaces to Hertz spaces and from Hardy spaces associated with the Beurling algebras to the Beurling algebrasin higher dimensions.     

On singular integrals along surfaces related to black spaces

Leth(t) be an arbitrary bounded radial function and let (x) be a real measurable and radial function defined onR ^n–1. Forx, yR ^n–1, we establish that the singular integral along surfacex (x, (x)):

Fixed point theorems in ordered abstract spaces

We extend some fixed point theorems in -spaces, obtaining extensions of the Banach fixed point theorem to partially ordered sets.