Displaying 381 – 400 of 673

Showing per page

Relations between weighted Orlicz and B M O φ spaces through fractional integrals

Eleonor Ofelia Harboure, Oscar Salinas, Beatriz E. Viviani (1999)

Commentationes Mathematicae Universitatis Carolinae

We characterize the class of weights, invariant under dilations, for which a modified fractional integral operator I α maps weak weighted Orlicz - φ spaces into appropriate weighted versions of the spaces B M O ψ , where ψ ( t ) = t α / n φ - 1 ( 1 / t ) . This generalizes known results about boundedness of I α from weak L p into Lipschitz spaces for p > n / α and from weak L n / α into B M O . It turns out that the class of weights corresponding to I α acting on weak - L φ for φ of lower type equal or greater than n / α , is the same as the one solving the problem for weak...

Schwartz kernel theorem in algebras of generalized functions

Vincent Valmorin (2010)

Banach Center Publications

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 G -generalized functions class are given. A straightforward relationship between the classical and the generalized versions...

Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications

José María Martell (2004)

Studia Mathematica

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...

Currently displaying 381 – 400 of 673