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On the resolvents of dyadic paraproducts.

María Cristina Pereyra — 1994

Revista Matemática Iberoamericana

We consider the boundedness of certain singular integral operators that arose in the study of Sobolev spaces on Lipschitz curves, [P1]. The standard theory available (David and Journé's T1 Theorem, for instance; see [D]) does not apply to this case becuase the operators are not necessarily Calderón-Zygmund operators, [Ch]. One of these operators gives an explicit formula for the resolvent at λ = 1 of the dyadic paraproduct, [Ch].

Some results on sequentially compact extensions

Maria Cristina Vipera — 1998

Commentationes Mathematicae Universitatis Carolinae

The class of Hausdorff spaces (or of Tychonoff spaces) which admit a Hausdorff (respectively Tychonoff) sequentially compact extension has not been characterized. We give some new conditions, in particular, we prove that every Tychonoff locally sequentially compact space has a Tychonoff one-point sequentially compact extension. We also give some results about extension of functions and about lattice properties of the family of all minimal sequentially compact extensions of a given space.

Wallman-type compaerifications and function lattices

Alessandro CaterinoMaria Cristina Vipera — 1988

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let F C ( X ) be a vector sublattice over which separates points from closed sets of X . The compactification e F X obtained by embedding X in a real cube via the diagonal map, is different, in general, from the Wallman compactification ω ( Z ( F ) ) . In this paper, it is shown that there exists a lattice F z containing F such that ω ( Z ( F ) ) = ω ( Z ( F z ) ) = e F X . In particular this implies that ω ( Z ( F ) ) e F X . Conditions in order to be ω ( Z ( F ) ) = e F X are given. Finally we prove that, if α X is a compactification of X such that C l α X ( α X X ) is 0 -dimensional, then there is an algebra A C a s t ( X ) such...

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