Damien Kreit

Characterizations of the elements of generalized Hölder-Zygmund spaces by means of their representation

Abstract In this paper, we give three characterizations of the elements of generalized Holder–Zygmund spaces. The first one, based on the Littlewood–Paley decomposition is already known, but the proof given here is much simpler. The second one, based on the wavelet decompositions generalizes a result obtained by Jaffard and Meyer. The third one uses generalized interpolation spaces. These results naturally extend the ones holding for the classical Holder–Zygmund spaces.

Generalized Pointwise Hölder Spaces Defined via Admissible Sequences

We introduce in this paper a generalization of the pointwise Holder spaces. We give alternative definitions of these spaces, look at their relationship with the wavelets, and introduce a notion of generalized Holder exponent.

A Refined Method for Estimating the Global Hölder Exponent

In this paper, we recall basic results we have obtained about generalized Holder spaces and present a wavelet characterization that holds under more general hypothesis than previously stated. This theoretical tool gives rise to a method for estimating the global Holder exponent which seems to be more precise than other wavelet-based approaches. This work should prove helpful for estimating long range correlations.