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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...

Smooth operators for the regular representation on homogeneous spaces

Severino Melo (2000)

Studia Mathematica

A necessary and sufficient condition for a bounded operator on L 2 ( M ) , M a Riemannian compact homogeneous space, to be smooth under conjugation by the regular representation is given. It is shown that, if all formal ’Fourier multipliers with variable coefficients’ are bounded, then they are also smooth. In particular, they are smooth if M is a rank-one symmetric space.

Some remarks on almost-positivity of ψ ⁢ do 's

Cesare Parenti, Alberto Parmeggiani (1998)

Bollettino dell'Unione Matematica Italiana

Per una classe di operatori pseudodifferenziali a caratteristiche multiple vengono date condizioni necessarie e sufficienti per la validità di stime dal basso «ottimali»

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