On Continuity of Generalized Riesz Potentials

On L Modulus of Continuity of Brownian Local times and Riesz Potentials

Abstract. This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on 3 closely related problems: (a) Limit theorem for a Brownian modulus of continuity involving Riesz potentials, where the limit law is an intricate Gaussian mixture. (b) Central limit theorems for the projections of L modulus of continuity for a 1-dimensional Brownian motion. (c) Ext...

On L2 Modulus of Continuity of Brownian Local times and Riesz Potentials by Aurélien Deya,

This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on three closely related problems: (a) Limit theorem for a Brownian modulus of continuity involving Riesz potentials, where the limit law is an intricate Gaussian mixture. (b) Central limit theorems for the projections of L2 modulus of continuity for a one-dimensional Brownian motion. (c) Extens...

On L2 modulus of continuity of Brownian local times and Riesz potentials

ec 2 00 5 Hölder - Sobolev regularity of the solution to the stochastic wave equation in dimension

We study the sample path regularity of the solution of a stochastic wave equation in spatial dimension d = 3. The driving noise is white in time and with a spatially homogeneous covariance defined as a product of a Riesz kernel and a smooth function. We prove that at any fixed time, a.s. the sample paths in the spatial variable belong to certain fractional Sobolev spaces. In addition, for any f...

Generalized Bessel and Riesz Potentials on Metric Measure Spaces

There is a rich literature on the study of Bessel and Riesz potentials on the Euclidean space R, see for example the books [23, 20, 1, 16] and the references therein. However, little is known on how to extend the Bessel and Riesz potentials to metric measure spaces in a reasonable way. This issue is interesting in that it is closely related with the study of various current topics, such as the ...