GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES

In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space F N^s(·)p(·),h(·),q(R³)with s(·)=4-2α-3/p(·).We prove global well-posedness result with small initial data belonging to FN^4-2α-3/p(·)p(·),h(·)q(R³).The result of this paper extends some recent work.     

BOUNDEDNESS OF MAXIMAL SINGULAR INTEGRALS

The authors study the singular integrals under the Hormander condition and the measure not satisfying the doubling condition. At first, if the corresponding singular integral is bounded from L2 to itself, it is proved that the maximal singular integral is bounded from L∞to RBMO except that it is infinite μ-a.e. on Rd. A sufficient condition and a necessary condition such that the maximal singular integral is bounded from L2 to itself are also obtained. There is a small gap between the two conditions.     

Low-molecular-weight photoresponsive supramulecular hydrogel based on a dicationic azobenzene-bridged pyridinium hydrogelator

Photoresponsive supramolecular hydrogel was fabricated from a small azobenzene-bridged dicationic pyridinium salt in the aqueous solution. The UV-vis light triggered reversible gel-sol transformation of such low-molecular-weight supramolecular hydrogel was systematically investigated through various analytical techniques.     

积域上粗糙核Marcinkiewicz积分的Lp有界性

本文证明了积域上的Marcinkiewicz积分算子μΩ是Lp( Rn× Rm) (11),而不需添加任何光滑性条件. 本文结果可视为Stein结果的一个改进.     

Hardy空间上一类带可变核的积分算子

本文给出了一类带可变核的奇异积分算子的（Hp,Lp）有界性及分数次积分算子的（Hp,Lq）有界性（0相似文献   

具有粗糙核的Marcinkiewicz积分交换子在齐次Herz空间中的有界性

该文证明了一类由Marcinkiewicz积分和BMO(Rn)函数生成的交换子在齐次Herz空间上的有界性．     

ON A HYPER HILBERT TRANSFORM＊＊＊＊

The authors define the directional hyper Hilbert transform and give ita mixed norm estimate. The similar conclusions for the directional fractional integral of one dimension are also obtained in this paper. As an application of the above results, the authors give the Lp-boundedness for a class of the hyper singular integrals and the fractional integrals with variable kernel. Moreover, as another application of the above results, the authors prove the dimension free estimate for the hyper Riesz transform. This is an extension of the related result obtained by Stein.     

ON BOUNDEDNESS OF HARDY-LITTLEWOOD MAXIMAL FUNCTION OPERATOR ON RIEMANNIAN MANIFOLDS

The authors construct a complete Riemannian manifold such that its Hardy-Littlewood maximal function operator is unbounded in $L^p$ for some p > 1.     

SOME PROPERTIES OF Λω^p（X,μ）

In this paper, we shall give a necessary and sufficient condition for which the dual of Λ _ω ^p (X, M, μ) (0<p<∞) is zero, and a necessary and sufficient condition for which Λ _ω ^p (X, M, μ), (0<p<1) is normable. Supported by 973 project (G1999075105), RFDP (20030335019) and ZJNSF(RC97017).     

Endpoint Estimates for Generalized Multilinear Fractional Integrals on the Non-homogeneous Metric Spaces

In this paper, some endpoint estimates for the generalized multilinear fractional integrals I_(α,m) on the non-homogeneous metric spaces are established.