Multilinear commutators of BMO functions and multilinear singular integrals with non-smooth kernels

This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.

Commutators of Lipschitz Functions and Singular Integrals with Non-Smooth Kernels on Euclidean Spaces

In this article, we obtain the LP-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.

SHARP MAXIMAL FUNCTION ESTIMATE AND WEIGHTED INEQUALITIES FOR MAXIMAL MULTILINEAR SINGULAR INTEGRALS

For maximal multilinear Calderon-Zygmund singular integral operators, the sharp maximal function estimate and some weighted norm inequalities are obtained.

A SHARP ESTIMATE ON THE DEGREE OF APPROXIMATION TO FUNCTIONS OF BOUNDED VARIATION BY CERTAIN OPERATORS

Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.

Boundedness for Multilinear Operators of Pseudo-Differential Operators

In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the Lp (1 p norm inequalities for the multilinear operators.

A MICRO-IMAGE FUSION ALGORITHM BASED ON REGION GROWING

Due to the limitation of Depth Of Field (DOF) of microscope, the regions which are not within the DOF will be blurring after imaging. Thus for micro-image fusion, the most important step is to identify the blurring regions within each micro-image, so as to remove their undesirable impacts on the fused image. In this paper, a fusion algorithm based on a novel region growing method is proposed for micro-image fusion. The local sharpness of micro-image is judged block by block, then blocks whose sharpness is lower than an adaptive threshold are used as seeds, and the sharpness of neighbors of each seed are evaluated again during the region growing until the blurring regions are identified completely. With the decreasing in block size, the obtained region segmentation becomes more and more accurate. Finally, the micro-images are fused with pixel-wise fusion rules. The experimental results show that the proposed algorithm benefits from the novel region segmentation and it is able to obtain fused micro-image with higher sharpness compared with some popular image fusion method.

BOUNDEDNESS OF MULTILINEAR FRACTIONAL INTEGRAL COMMUTATORS

By introducing a kind of maximal operator of fractional order associated with the mean Luxemburg norm and using the technique of Sharp function,multilinear commutators of fractional integral operator with vector symbol b=(b 1,...,b m)defined byI b αf(x)=∫ R∏mj=1(b j(x)-b j(y))1｜x-y｜ n-αf(y)dyare considered.The following priori estimates are proved.For 1<p<∞,there exists a constant c such that‖I b αf‖ Lp(Rn)≤c‖b‖‖M L(logL) 1r,α(f)‖ Lp(Rn),So‖I b αf‖ Lq(Rn)≤c‖b‖‖f‖ Lp(Rn),where 1<p<nα,1q=1p-αn,0<α<n,and supt>01Φ1t｜｛y∈Rn:｜I b αf(y)｜>t｝｜ 1q≤ c supt>01Φ1t｜｛y∈Rn:M L(logL) 1r,α(‖b‖f)(y)>t｝｜ 1q,where ‖b‖=∏ m j=1‖b j‖ Osc expL r j,Φ(t)=t(1+log+t) 1r,1r=1r 1+...+1r m, M L(logL) 1r,α is an Orlicz type maximal operator.

Endpoint Estimates for Commutators of Fractional Integrals Associated to Operators with Heat Kernel Bounds

Let L be the infinitesimal generator of an analytic semigroup on L;（R;）with pointwise upper bounds on heat kernel,and denote by L;the fractional integrals of L.For a BMO function b（x）,we show a weak type Llog L estimate of the commutators [b,L;]（f）(x) = b（x）L;（f）(x)-L;（bf）(x).We give applications to large classes of differential operators such as the Schr¨odinger operators and second-order elliptic operators of divergence form.

Commutators of Singular Integral Operators Related to Magnetic Schrdinger Operators

Let A=-（ -ia）·（ -ia）＋V be a magnetic Schrodinger operator on L^2（R^n）,n〉2,where a：=（a1,…,an）∈Lloc^2（R^n,R^n） and 0≤V ∈Lloc^1（R^n）.In this paper, we show that for a function b in Lipschitz space Lipa（R^n）with a∈（0,1）,the commutator [b,V1/2A^-1/2]is bounded from L^p（R^n）to L^q（R^n）,where p,q∈（1,2] and 1/p-1/q=a/n.

Weak estimates for commutators of fractional integral operators

By introducing a kind of maximal operator of the fractional order associated with the mean Luxemburg norm and using the technique of the sharp function,the weak type LlogL estimates for the commutators of the fractional integral operator and the related maximal operator are established.

Weighted estimates for the multilinear commutators of the Littlewood-Paley operators

In this paper, weighted Lp estimates and sharp weighted endpoint estimates for the mul-tilinear commutators of the Littlewood-Paley operators are established.

Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integral

Let μ be the n-dimensional Marcinkiewicz integral and μb the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A∞ and 0 〈 p 〈 ∞,｜｜μ（f）｜｜LP（ω）≤C｜Mf｜LP（ω） and ｜｜μb（f）｜｜LP（ω）≤C｜｜ML（log L）^1/r f｜｜LP（ω）.The weighted weak L（log L）^1/r -type estimate is also established when p=1 and ω∈A1.

Multilinear Singular Integral Operators with Generalized Kernels and Their Multilinear Commutators

In this paper, the authors study a class of multilinear singular integral operators with generalized kernels and their multilinear commutators with BMO functions. By establishing the sharp maximal estimates, the boundedness on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces is obtained, respectively. Moreover, the endpoint estimate of this class of mutilinear singular integral operators is also established. These results can improve the corresponding known results of classical multilinear Calder6n-Zygmund operators and multilinear Calderon-Zygmund operators with Dini type kernels.

An equivalent characterization of BMO with Gauss measure

Let γ be the Gauss measure on Rn. We establish a Calderon- Zygmund type decomposition and a John-Nirenberg type inequality in terms of the local sharp maximal function and the median value of function over cubes. As an application, we obtain an equivalent characterization of known BMO space with Gauss measure.

Weighted L^p Estimates for Maximal Commutators of Multilinear Singular Integrals

This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T∑b^＊ and TПb^＊ which are generalized by a weighted BMO function b and a multilinear singular integral operator T, respectively. As applications, some commutator theorems are established.

Weighted Endpoint Estimates for Maximal Commutators Associated with the Sections

We prove endpoint estimates for maximal commutators for a class of singular integral operators related to the real analysis of the Monge Ampere equation.

Rainbow k-connectivity of Random Bipartite Graphs

A path in an edge-colored graph G is called a rainbow path if no two edges of the path are colored the same color.The minimum number of colors required to color the edges of G such that every pair of vertices are connec ted by at least k internally ver tex-disjoint rainbow paths is called the rainbow k-connectivity of the graph G,denoted by rck(G).For the random graph G(n,p),He and Liang got a sharp threshold function for the property rck(G(n,p))≤d.For the random equi-bipartite graph G(n,n,p),Fujita et.al.got a sharp threshold function for the property rck(G(n,n,p))≤3.They also posed the following problem:For d≥2,determine a sharp threshold function for the property rck(G)≤d,where G is another random graph model.This paper is to give a solution to their problem in the general random bipartite graph model G(m,n,p).

Weighted Norm Inequalities for Marcinkiewicz Integrals with Non-Smooth Kernels on Spaces of Homogeneous Type

In this article,we obtain some weighted estimates for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type.The weightωconsidered here belongs to the Muckenhoupt’s class A_(∞).Moreover,weighted estimates for commutators of BMO functions and Marcinkiewicz integrals are also given.