A P ] 2 3 O ct 2 00 3 Hölder-Zygmund regularity in algebras of generalized functions

  title={A P ] 2 3 O ct 2 00 3 H{\"o}lder-Zygmund regularity in algebras of generalized functions},
  author={G{\"u}nther H{\"o}rmann},
We introduce an intrinsic notion of Hölder-Zygmund regularity for Colombeau generalized functions. In case of embedded distributions belonging to some Zygmund-Hölder space this is shown to be consistent. The definition is motivated by the well-known use of Littlewood-Paley decomposition in characterizing Hölder-Zygmund regularity for distributions. It is based on a simple interplay of differentiated convolution-mollification with wavelet transforms, which directly translates wavelet estimates… CONTINUE READING