Topology on new sequence spaces defined with wavelet leaders

Using wavelet leaders instead of wavelet coefficients, new sequence spaces of type SνSν are defined and endowed with a natural topology. Some classical topological properties are then studied; in particular, a generic result about the asymptotic repartition of the wavelet leaders of a sequence in LνLν is obtained. Eventually, comparisons and links with Oscillation spaces are also presented as well as with SνSν spaces.