estimates for weakly strongly singular integral operators on spaces of homogeneous type
Hardy spaces and oscillatory singular integrals.
Heat kernel estimates for critical fractional diffusion operators
We construct the heat kernel of the 1/2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.
Heat kernel estimates for the Dirichlet fractional Laplacian
We consider the fractional Laplacian on an open subset in with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such a Dirichlet fractional Laplacian in open sets. This heat kernel is also the transition density of a rotationally symmetric -stable process killed upon leaving a open set. Our results are the first sharp twosided estimates for the Dirichlet heat kernel of a non-local operator on open sets.
Higher order Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator
The aim of this paper is to extend the study of Riesz transforms associated to Dunkl Ornstein-Uhlenbeck operator considered by A. Nowak, L. Roncal and K. Stempak to higher order.
Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations
This paper is concerned with the Hölder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth...
Hölder weight estimates of Riesz-Bessel singular integrals generated by a generalized shift operator.
Hypoellipticité et paramétrix pour des opérateurs pseudodifférentiels à caractéristiques doubles