We present a framework that yields a variety of weighted and vector-valued estimates for maximally modulated Calderón-Zygmund singular (and maximal singular) integrals from a single a priori weak type unweighted estimate for the maximal modulations of such operators. We discuss two approaches, one based on the good-λ method of Coifman and Fefferman [CF] and an alternative method employing the s...

BACKGROUND AND PURPOSE In fat embolism, free fatty acid is more toxic than neutral fat in terms of tissue damage. We evaluated the hyperacute embolic effects of triolein and oleic acid in cat brains by using MR imaging and electron microscopy. METHODS T2-weighted imaging, diffusion-weighted imaging, and contrast-enhanced T1-weighted imaging were performed in cat brains after the injection of ...

Abstract We study a wave equation in dimension $d\in \{1,2\}$ with multiplicative space-time Gaussian noise. The existence and uniqueness of the Stratonovich solution is obtained under some conditions imposed on strategy to develop Strichartz-type estimates for kernel weighted Besov spaces, by which we can prove well-posedness an associated Young-type equation. Those Strichartz bounds are indep...

We obtain the characterizations of commutators several versions maximal functions on spaces homogeneous type. In addition, with aid interpolation theory, we provide weighted version commutator theorems by establishing new BMO space. Finally, a concrete example shows that local also has an independent interest.

Recall that in an earlier paper by one of the authors DonaldsonThomas type invariants were expressed as certain weighted Euler characteristics of the moduli space. The Euler characteristic is weighted by a certain canonical Z-valued constructible function on the moduli space. This constructible function associates to any point of the moduli space a certain invariant of the singularity of the sp...

where the coefficients are entire functions. In [8], equations of the form (1) with coefficients in weighted Bergman or Hardy spaces are studied. The direct problem is proved, that is, if the coefficients aj(z), j = 0, ..., k − 1 of (1) belong to the weighted Bergman space, then all solutions are of finite order of growth and belong to weighted Bergman space. The inverse problem is also investi...

This paper presents necessary and sufficient conditions for onand off-diagonal transition probability estimates for random walks on weighted graphs. On the integer lattice and on may fractal type graphs both the volume of a ball and the mean exit time from a ball is independent of the centre, uniform in space. Here the upper estimate is given without such restriction and two-sided estimate is g...