Bifurcation of periodic points and normal form theory in reversible diffeomorphisms
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].
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.
Let be a vector sublattice over which separates points from closed sets of . The compactification obtained by embedding in a real cube via the diagonal map, is different, in general, from the Wallman compactification . In this paper, it is shown that there exists a lattice containing such that . In particular this implies that . Conditions in order to be are given. Finally we prove that, if is a compactification of such that is -dimensional, then there is an algebra such...
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