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.     

ON A KAHLER VERSION OF CHEEGER-GROMOLL-PERELMAN＇S SOUL THEOREM

In this note, we will prove a Kahler version of Cheeger-Gromoll-Perelman＇s soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point.     

THEOREMS OF BARTH-LEFSCHETZ TYPE ON KAHLER MANIFOLDS WITH PARTIALLY POSITIVE CURVATURE

The author obtains the theorems of Barth-Lefschetz type on Kahler manifolds with partially positive bisectional curvature without the assumption of nonnegative bisectional curvature. Some applications of the results to holomorphic mappings are given.     

On the classification of positive quaternionic Kähler manifolds with b 4 = 1

Let M be a positive quaternionic Kahler manifold of dimension 4m. We already showed that if the symmetry rank is greater than or equal to [m/2] ＋ 2 and the fourth Betti number b4 is equal to one, then M is isometric to HPm. The goal of this paper is to report that we can improve the lower bound of the symmetry rank by one for higher even-dimensional positive quaternionic Kahler manifolds. Namely, it is shown in this paper that if the symmetry rank of M with b4（M） = 1 is greater than or equal to m/2 ＋ 1 for m ≥ 10, then M is isometric to HPm. One of the main strategies of this paper is to apply a more delicate argument of Frankel type to positive quaternionic Kahler manifolds with certain symmetry rank.     

Immortal solution of the Ricci flow

For any complete noncompact Kahler manifold with nonnegative and bounded holomorphic bisectional curvature, we provide the necessary and sufficient condition for the immortal solution to the Ricci flow.     

A Remark on Steinness

In this paper, the authors prove that if Mn is a complete noncompact Kahler manifold with a pole p, and its holomorphic bisectional curvature is asymptotically non-negative to p, then it is a Stein manifold.     

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     

Ho1der Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets

In this paper we establish sharp H/51der estimates of harmonic functions on a class of connected post critically finite （p.c.f.） self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some weU-known examples, such as the Sierpinski gasket, the unit interval, the level 3 Sierpinski gasket, the hexagasket, the 3-dimensional Sierpinski gasket, and the Vicsek set are also considered.     

Bubble tree convergence for the harmonic sequence of harmonic surfaces in ℂℙ n

We show that any harmonic sequence determined by a harmonic map from a compact Riemannian surface M to CP^n has a terminating holomorphic （or anti-holomorphic） map from M to CP^n, or a ＂bubble tree limit＂ consisting of a harmonic map f： M → CP^n and a tree of bubbles hλ^μ： S^2 --→ CP^n.     

Some Properties of the Beurling-Ahlfors Extension

In this paper, we study the Beurling-Ahlfors extensions and prove two results. The first variation of the Beurling-Ahlfors extension is not always harmonic; the Beurling-Ahlfors extension of a quasisymmetric mapping is not always harmonic.     

THE ELLIPSOID ARTIFICIAL BOUNDARY METHOD FOR THREE-DIMENSIONAL UNBOUNDED DOMAINS

The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived explicitly in terms of an infinite series. Then the well-posedness of the coupled variational problem is obtained. It is found that error estimates derived depend on the mesh size, truncation term and the location of the artificial boundary. Three numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.     

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.     

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 ωφλ^r（f,t）wφ^s（0≤λ≤1）are given. The relation between derivatives of combinations of Gamma operators and smoothness of derivatives of functions is also investigated.     

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 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.     

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.     

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.