Remarks on g-functions on H^n

In this paper, the authors study some properties of Littlewood-Paley g-functions gψ（f）,Lusin area functions Sψ,α（f） and Littlewood-Paley gψ^＊,λ（f） functions defined on H^n, where α,λ 〉 0 and ψ, f are suitable functions. They are the generalization of the corresponding operators on R^n.     

Tilting bundles on orders on ℙd

We introduce a class of orders on ?^d called Geigle-Lenzing orders and show that they have tilting bundles. Moreover we show that their module categories are equivalent to the categories of coherent sheaves on Geigle- Lenzing projective spaces introduced in [HIMO].     

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Injectivity sets for spherical means on ℝ n and on symmetric spacesand on symmetric spaces

A complex Radon measure μ on ℝ ⁿ is said to be of at most exponential-quadratic growth if there exist positive constants C and α such that . Let X_exp denote the space of all complex Radon measure on ℝ ⁿ of at most exponential-quadratic growth. Using elementary methods, we obtain injectivity sets for spherical means for X_exp. We also discuss similar results for symmetric spaces.     

A note on certain square functions on product spaces

We study certain square functions on product spaces Rn × Rm, whose integral kernels are obtained from kernels which are homogeneous in each factor Rn and Rm and locally in L(log L) away from Rn × {0} and {0} × Rm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on Lp(Rn × Rm)(P > 1) for Ω∈ e Llog L(Sn-1 × Sm-1) satisfying the cancellation condition.     

A note on Haj?asz-Sobolev spaces on fractals

We introduce Haj?asz-Sobolev spaces involving walk dimensions on subsets of that will generally be fractals. The relationship between this kind of new space and the Besov space of Jonsson and Wallin is investigated. The (compact) embedding theorems for Haj?asz-Sobolev spaces are obtained.     

Isomorphism on Hypergroups

ＩｓｏｍｏｒｐｈｉｓｍｏｎＨｙｐｅｒｇｒｏｕｐｓ钟育彬ＩｓｏｍｏｒｐｈｉｓｍｏｎＨｙｐｅｒｇｒｏｕｐｓ￥ＺｈｏｎＹｕＢｉｎ（Ｄｅｐｔ．ｏｆＭａｔｈｓ．，ＧｕａｎｇｚｈｏｕＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｐｅｐｅｒｇｉｖｅｓｓ...     

A Remark on Pl Type Interpolation on Non-Uniformly Distributed Nodes on the Unit Circle

In this paper we study the problem of explicit representation and convergence of P′al type(0;1) interpolation and its converse, with some additional conditions,on the non-uniformly distributed nodes on the unit circle obtained by projecting the interlaced zeros of Pn(x) and P′n(x) on the unit circle. The motivation to this problem can be traced to the recent studies on the regularity of Birkhoff interpolation and P′al type interpolations on non-uniformly distributed zeros on the unit circle.     

Composition Operators on Hardy–Orlicz Spaces on the Ball

We give embedding theorems for Hardy–Orlicz spaces on the ball and then apply our results to the study of the boundedness and compactness of composition operators in this context. As one of the motivations of this work, we show that there exist some Hardy–Orlicz spaces, different from H ^∞, on which every composition operator is bounded.     

Note on Magic Squares and Magic Cubes on Abelian Groups

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A Remark on Partly Dissipative Reaction Diffusion Systems on IR~n

The long time behavior of the solutions of some partly dissipative reaction diffusion systems is studied.We prove the existence of a compact(L~2×L~2-H~1×L~2)attractor for a partly dissipative reaction diffusion system in R~n.This improves a previous result obtained by A.Rodrigues-Bernal and B.Wang concerning the existence of a compact(L~2×L~2-L~2×L~2)attractor for the same system.     

A Note on Property of Cauchy Integral on Classical Domains

In[1],ZhengXueanprovedthat:letRI(n×n)befirstclassicaldomain,Unbecharacteris-ticboundaryofRI,x∈Un,f(x)∈L2(Un).Asz=rx(0≤r<1)→x,Cauchyintegral∫Unf(y)det(I-zy′)-ndyconvergetoafunctioninL2(Un).Inthispaper,wewillfacusourselfonCauchyintegralofL2onclassicaldomains[2]andgetsomeproperties.Themainresultisfollowing:Theorem　LetRbeoneofclassicaldomains,LbecharacteristicboundaryofR,f∈L2(L),H(z,ξ)beCauchykernelofRandF(z)=∫Lf(u)H(z,u)u　z∈R,(1)wheretherightisLebesgueintegral;uist…     

Remarks on “Quasi-contraction on a cone metric space”

Recently, D. Ili? and V. Rako?evi? [D. Ili?, V. Rako?evi?, Quasi-contraction on a cone metric space, Appl. Math. Lett. (2008) doi:10.1016/j.aml.2008.08.011] proved a fixed point theorem for quasi-contractive mappings in cone metric spaces when the underlying cone is normal. The aim of this paper is to prove this and some related results without using the normality condition.     

Some remarks on Kong-Liu’s conjecture on Lorentzian metrics

For a(1+3)-dimensional Lorentzian manifold(M,g),the general form of solutions of the Einstein field equations takes that of type I,II,or III.For type I,there is a known result in Gu(2007).In this paper,we try to find the necessary and sufficient conditions for the Lorentzian metric to take the form of types II and III,and we show how to construct the new coordinate system.     

Comment on “A note on a study on an integrable system of coupled KdV equations”

We analyze the note by Muraved [A note on A study on an integrable system of coupled KdV equations [1], Commun Nonlinear Sci Numer Simulat. doi:10.1016/j.cnsns.2010.06.018]. Author tried to show that our approach is curious. We demonstrate that, author has not shown any error and presented a curious note.     

A Note on Commutators with Power Central Values on Lie Ideals

This note proves that, if R is a prime ring of characteristic 2 with d a derivation of R and L a noncentral Lie ideal of R such that [d（u）,u]^n is central, for all u ∈ L, then R must satisfy s4, the standard identity in 4 variables. The case where R is a semiprime ring is also examined by the authors. The results of the note improve Carini and Filippis＇s results.     

Bilinear Operators on Herz-type Hardy Spaces on Locally Compact Vilenkin Groups

Let G be a locally compact Vilenkin group. In this paper the authors study the boundedness of bilinear operators B（f, g） given by finite sums of products of Calderdn-Zygmund operators in Herz space and Herz-type Hardy space on G. And an example, the boundedness from the products of Herz space to Herz-type Hardy space is given in the last section.     

Positive Operators à la Aumann-Shapley on Spaces of Functions on D-Lattices

Let L be a σ-complete D-lattice and BV the AL-space of all realvalued, null in zero, functions on L of bounded variation. We prove the existence of a continuous Aumann-Shapley operator on the closed subspace of BV generated by powers of nonatomic σ-additive positive modular measures on L. The integral representation of on a class of functions that correspond to measure games is also exhibited. Dedicated to Professor Paolo De Lucia on the occasion of his 70th birthday.     

Lectures on Time Series

§1.Introduction to Fourier Analysis of Data Consider first a discrete time scalar system on which we make observation y(t),t=1,…,T.Thus we have chosen the time unit as the interval between observations.be as-sume that y(t)Is generated by a stationary process. It will always be assumed that y(t)is generated by an ergodic process.Thusif φ is a measurable function defined on the measure space of all realizations ofthe process and