Let $\mathcal{M}$ be the bilinear Hardy-Littlewood maximal function and $\vec{b}=(b,b)$ a collection of locally integrable functions. In this paper, authors establish characterizations weighted {\rm BMO} space in terms several different commutators function, respectively; these include iterated commutator $\mathcal{M}_{\Pi \vec{b}}$, linear $\mathcal{M}_{\Sigma\vec{b}}$, $[\Pi \vec{b},\mathcal{...

OBJECTIVE We previously showed that NAD(P)H oxidase deficiency significantly reduces atherosclerosis in apoE(-/-) mice. The present study was designed to determine the relative contribution of monocyte/macrophage versus vascular wall cell NAD(P)H oxidase to atherogenesis in this model. METHODS AND RESULTS Cell-specific NAD(P)H oxidase inhibition was achieved via allogenic, sex-mismatched bone...

PURPOSE This study examined the peripapillary choroidal thickness (PCT) in nonarteritic ischemic optic neuropathy (NAION) in comparison to contralateral eyes and normal eyes. METHODS We used enhanced depth imaging spectral-domain optical coherence tomography to image the optic nerve head of 20 NAION, 10 contralateral eyes, and 102 normal eyes. Following compensation, the scans were manually d...

R 2 are explored. Mild conditions are imposed on the triangulations which prevent them from deterioration and at the same time allow for a lot of flexibility and, in particular, arbitrarily sharp angles. It is shown that such anisotropic Franklin systems are Schauder bases for C and L1, and unconditional bases for Lp (1 < p < ∞) and the corresponding Hardy spaces H1. It is also proved that the ...

X iv :0 70 9. 42 29 v1 [ m at h. FA ] 2 6 Se p 20 07 An Extrapolation of Operator Valued Dyadic Paraproducts Tao MEI 1 Abstract We consider the dyadic paraproducts πφ on T associated with an M-valued function φ. Here T is the unit circle and M is a tracial von Neumann algebra. We prove that their boundedness on L(T, L(M)) for some 1 < p < ∞ implies their boundedness on L(T, L(M)) for all 1 < p ...

Boundedness properties for pseudodifferential operators with symbols in the bilinear Hörmander classes of sufficiently negative order are proved. The results are obtained in the scale of Lebesgue spaces, and in some cases, end-point estimates involving weak-type spaces and BMO are provided as well. From the Lebesgue space estimates, Sobolev ones are then easily obtained using functional calculu...

In this paper, we study inhomogeneous Dirichlet problems for elliptic equations in divergence form. Optimal regularity requirements on the coefficients and domains for the W 1,p (1 < p < ∞) estimates are obtained. The principal coefficients are supposed to be in the John-Nirenberg space with small BMO semi-norms. The domain is supposed to have Lipschitz boundary with small Lipschitz constant. T...

This paper is devoted to the decomposition of an image f into u + v, with u a piecewise-smooth or “cartoon” component, and v an oscillatory component (texture or noise), in a variational approach. Meyer [Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, Univ. Lecture Ser. 22, AMS, Providence, RI, 2001] proposed refinements of the total variation model (Rudin, Osher, an...