A New Estimate for Bochner-Riesz Operators at the Critical Index on Weighted Hardy Spaces

Let w be a Muckenhoupt weight and Hwp （JRn） be the weighted Hardy space. In this paper, by using the atomic decomposition of Hwp（Rn）, we will show that the Bochner-Riesz operators TRδ are bounded from Hwp（Rn） to the weighted weak Hardy spaces WHwp （Rn） for 0 〈 p 〈 1 and δ = n/p- （n ＋ 1）/2. This result is new even in the unweighted case.     

Boundedness for Commutators of Approximate Identities on Weighted Morrey Spaces

The aim of this paper is to set up the weighted norm inequalities for commutators generated by approximate identities from weighted Lebesgue spaces into weighted Morrey spaces     

Weighted Approximation by Left Quasi-interpolants of Derivatives of Gamma Operators

In order to obtain much faster convergence, Miiller introduced the left Gamma quasi- interpolants and obtained an approximation equivalence theorem in terms of 2r wφ （f,t）p. Cuo extended the MiiUer＇s results to wφ^24 （f, t）∞. In this paper we improve the previous results and give a weighted approximation equivalence theorem.     

VANISHING THEOREMS FOR ACH KAHLER MANIFOLDS AND HARMONIC MAPS

We discuss a class of complete Kaihler manifolds which are asymptotically complex hyperbolic near infinity. The main result is vanishing theorems for the second L2 cohomology of such manifolds when it has positive spectrum. We also generalize the result to the weighted Poincare inequality case and establish a vanishing theorem provided that the weighted function p is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighted Poincare inequality.     

Weighted Estimates for the Maximal Commutator of Singular Integral Operator on Spaces of Homogeneous Type

Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable.     

BOUNDEDNESS OF COMMUTATORS OF GENERALIZED FRACTIONAL INTEGRAL OPERATORS ON WEIGHTED HERZ-TYPE HARDY SPACES

In this paper, we study the boundedness of higher order commutators of gen- eralized fractional integral operators on weighted Lp spaces and Herz-type Hardy spaces.     

One Nonparabolic End Theorem on Kahler Manifolds

In this paper, the complete noncompact Kahler manifolds satisfying the weighted Poincare inequality are considered and one nonparabolic end theorem which generalizes Munteanu＇s result is obtained.     

A remark on strong law of large numbers for weighted U-statistics

Let {X,Xn; n ≥ 1} be a sequence of i.i.d.random variables with values in a measurable space(S,S) such that E|h(X1,X2,...,Xm)| ∞,where h is a measurable symmetric function from Sminto R =(-∞,∞).Let {wn,i1,i2,...,im; 1 ≤ i1 i2 ··· im ≤ n,n ≥ m} be a matrix array of real numbers.Motivated by a result of Choi and Sung(1987),in this note we are concerned with establishing a strong law of large numbers for weighted U-statistics with kernel h of degree m.We show that lim n→∞m!(n-m)!n!1≤i1i2···im≤n wn,i1,i2,...,im(h(Xi1,Xi2,...,Xim)-θ)=0 a.s.whenever supn≥mmax1≤i1i2···im≤n|wn,i1,i2,...,im|∞,whereθ=Eh(X1,X2,...,Xm).The proof of this result is based on a new general result on complete convergence,which is a fundamental tool,for array of real-valued random variables under some mild conditions.     

SHARP MAXIMAL FUNCTION ESTIMATES FOR MULTILINEAR SINGULAR INTEGRALS WITH NON-SMOOTH KERNELS

In this article we obtain weighted norm estimates for multilinear singular integrals with non-smooth kernels and the boundedness of certain multilinear commutators by making use of a sharp maximal function.     

Weighted Lipschitz Estimate for Commutator of Bochner-Riesz Operators on Weighted Morrey Spaces

In this paper, we will use a method of sharp maximal function approach to show the boundedness of commutator [b,TδR] by Bochner-Riesz operators and the function b on weighted Morrey spaces Lp,κ(ω) under appropriate conditions on the weight ω, where b belongs to Lipschitz space or weighted Lipschitz space.     

Complex Interpolation of Weighted Besov and Lizorkin–Triebel Spaces

We study complex interpolation of weighted Besov and Lizorkin–Triebel spaces.The used weights w0,w1 are local Muckenhoupt weights in the sense of Rychkov.As a first step we calculate the Calder′on products of associated sequence spaces.Finally,as a corollary of these investigations,we obtain results on complex interpolation of radial subspaces of Besov and Lizorkin–Triebel spaces on Rd.     

Optimal integrability of some system of integral equations

We obtain the optimal integrability for positive solutions of the Euler-Lagrange system of the weighted Hardy-Littlewood-Sobolev inequality in R^n ：{u（x）=1/｜x｜^α｜∫R^n v（y）^q｜y｜^β｜x-y｜^λdy,v（x）=1/｜x｜^β∫R^n u（y）^p｜y｜^α｜x-y｜^λdy.C. Jin and C. Li [Calc. Var. Partial Differential Equations, 2006, 26： 447-457] developed some very interesting method for regularity lifting and obtained the optimal integrability for p, q 〉 1. Here, based on some new observations, we overcome the difficulty there, and derive the optimal integrability for the case of p, q ≥1 and pq ≠1. This integrability plays a key role in estimating the asymptotic behavior of positive solutions when ｜x｜ →0 and when ｜x｜→∞.     

Non-simultaneous Blow-up Criteria for Localized Parabolic Equations

This paper deals with blow-up solutions for parabolic equations coupled via localized exponential sources, subject to homogeneous Dirichlet boundary con- ditions. The criteria are proposed to identify simultaneous and non-simultaneous blow-up solutions. The related classification for the four nonlinear parameters in the model is optimal and complete.     

WEIGHTED NONLINEAR REGRESSION

Minimization of the weighted nonlinear sum of squares of differences may be converted to the minimization of sum of squares. The Gauss-Newton method is recalled and the length of the step of the steepest descent method is determined by substituting the steepest descent direction in the Gauss-Newton formula. The existence of minimum is shown.     

Equivalent theorems on simultaneous approximation by combinations of Gamma operators

In this paper,some equivalent theorems on simultaneous approximation for combinations of Gamma operators by weighted moduli of smoothness ωr(4)λ(f,t)w(4)s(O≤λ≤1)are given.The relation between derivatives of combinations of Gamma operators and smoothness of derivatives of functions is also investigated.     

Weighted norm inequalities of the maximal commutator of quasiradial Bochner-Riesz operators

In this paper, we obtain certain Lpw(Rn)-mapping properties for the maximal operator associated with the commutators of quasiradial Bochner-Riesz means with index δ under certain surface condition on Σed , provided that δ (n-1)/2, b ∈ BMO(Rn), 1 p ∞ and w ∈ A1 . Moreover, if δ (n-1)/2, then we prove that the above maximal operator admits weak type (H1w(Rn), L1w(Rn))-mapping properties for b ∈ BMO(Rn) and w ∈ A1 under the surface condition on Σed .     

Adiabatic limit in the Ginzburg-Landau and Seiberg-Witten equations

We study an adiabatic limit in (2 + 1)-dimensional hyperbolic Ginzburg-Landau equations and 4-dimensional symplectic Seiberg-Witten equations. In dimension 3 = 2+1 the limiting procedure establishes a correspondence between solutions of Ginzburg-Landau equations and adiabatic paths in the moduli space of static solutions, called vortices. The 4-dimensional adiabatic limit may be considered as a complexification of the (2+1)-dimensional procedure with time variable being “complexified.” The adiabatic limit in dimension 4 = 2+2 establishes a correspondence between solutions of Seiberg-Witten equations and pseudoholomorphic paths in the moduli space of vortices.     

Extending symmetric determinantal quartic surfaces

We give an explicit construction for the extension of a symmetric determinantal quartic K3 surface to a Fano sixfold. Remarkably, the moduli of the sixfold extension are in one-to-one correspondence with the moduli of the quartic surface. As a consequence, we determine a 16-parameter family of surfaces of general type with \(p_g=1, q=0\) and \(K^2=2\) as weighted complete intersections inside Fano sixfolds.     

一类不定方程组的解的个数

本文将证明以下结论:设m为正整数,当(a,c,δ)取(m,m+1,-1),(m,m+ 2,-2),(m,m+4,-4),或者(m+2,m,2)时,联立的不定方程组■的正整数解(x,y,z)的个数不超过1。     

Equivariant cohomology of certain moduli of weighted pointed rational curves

We determine the action of the product of symmetric groups on the cohomology of certain moduli of weighted pointed rational curves. The moduli spaces that we study are of stable rational curves with m + n marked points where the first m marked points are distinct from all the others where as the last n may coincide among themselves. We give a recipe for calculating the equivariant Poincaré polynomials and list them for small m and n.