Régularité lipschitzienne et solutions de l'équation des ondes sur une variété riemannienne compacte
We characterize the class of weights, invariant under dilations, for which a modified fractional integral operator maps weak weighted Orlicz spaces into appropriate weighted versions of the spaces , where . This generalizes known results about boundedness of from weak into Lipschitz spaces for and from weak into . It turns out that the class of weights corresponding to acting on weak for of lower type equal or greater than , is the same as the one solving the problem for weak...
A new approach to the generalization of Schwartz’s kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of -generalized functions class are given. A straightforward relationship between the classical and the generalized versions...
In the context of the spaces of homogeneous type, given a family of operators that look like approximations of the identity, new sharp maximal functions are considered. We prove a good-λ inequality for Muckenhoupt weights, which leads to an analog of the Fefferman-Stein estimate for the classical sharp maximal function. As a consequence, we establish weighted norm estimates for certain singular integrals, defined on irregular domains, with Hörmander conditions replaced by some estimates which do...