Fractional Sobolev embeddings and algebra property: A dyadic view
Fractional Sobolev embeddings and algebra property: A dyadic view
This paper revisits classical fractional Sobolev embedding theorems and the algebra property of the fractional Sobolev space $H^s(\mathbb{R})$ by means of Haar functions and dyadic decompositions. The aim is to provide an alternative, hands-on approach without Fourier transform that may be transferred to settings where the latter is not available. …