SOME ENDPOINT ESTIMATES FOR COMMUTATORS OF θ-TYPE CALDERóN-ZYGMUND OPERATORS

In this note, the authors prove that the commutator Tb, generated by θ-type Calderon-Zygmund operator T and a Lipschitz function b is bounded from LP（R^n） intoLip（β_n/p）（R^n） and also maps from Ln/β （R^n） into BMO（R^n）.

The Boundedness of the Commutator for Riesz Potential Associated with Schr dinger Operator on Morrey Spaces

Let L=-△＋V be the Schrodinger operator on Rd, where？is the Laplacian on Rd and V ≠=0 is a nonnegative function satisfying the reverse Holder’s inequality. The authors prove that Riesz potential Iβand its commutator [b,Iβ] associated with L map from Mp,qα,v into Mp1,q1α,v .

A Behavioral Authentication Method for Mobile Based on Browsing Behaviors

The passwords for unlocking the mobile devices are relatively simple,easier to be stolen,which causes serious potential security problems.An important research direction of identity authentication is to establish user behavior models to authenticate users.In this paper,a mobile terminal APP browsing behavioral authentication system architecture which synthesizes multiple factors is designed.This architecture is suitable for users using the mobile terminal APP in the daily life.The architecture includes data acquisition,data processing,feature extraction,and sub model training.We can use this architecture for continuous authentication when the user uses APP at the mobile terminal.

Two Weighted BMO Estimates for the Maximal Bochner-Riesz Commutator

In this note, the author prove that maximal Bocher-Riesz commutator Bδ,＊^b generated by operator Bδ,＊ and function b∈ BMO（ω） is a bounded operator from L^p（μ） into L^p（ν）, where w∈ （μν^- 1）^1/p,μ,v ∈ Ap for 1 〈 p 〈 ∞. The proof relies heavily on the pointwise estimates for the sharp maximal function of the commutator Bδ,＊^b.

Multiple weighted estimates for maximal vector-valued commutator of multilinear Calderon-Zygmund singular integrals

This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued commutators are also established. By the weighted estimates of a class of new variant maximal operator, Cotlar＇s inequality and the sharp maximal flmction estimates, multiple weighted strong estimates and weak estimates for maximal vector-valued singular integrals of multilinear operators and those for maximal vector-valued commutator of multilinear singular integrals are obtained.

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.

Long Time Well-Posedness of the MHD Boundary Layer Equation in Sobolev Space

In this paper, we study the long time well-posedness of 2-D MHD boundary layer equation. It was proved that if the initial data satisfies■,then the life span of the solution is at least of order ε2-η for η > 0.