On the -differentiability of certain classes of functions

  • Giovanni Alberti

    Università di Pisa, Italy
  • Stefano Bianchini

    SISSA-ISAS, Trieste, Italy
  • Gianluca Crippa

    Universität Basel, Switzerland


We prove the -differentiability at almost every point for convolution products on of the form , where is bounded measure and is a homogeneous kernel of degree . From this result we derive the -differentiability for vector fields on whose curl and divergence are measures, and also for vector fields with bounded deformation.

Cite this article

Giovanni Alberti, Stefano Bianchini, Gianluca Crippa, On the -differentiability of certain classes of functions. Rev. Mat. Iberoam. 30 (2014), no. 1, pp. 349–367

DOI 10.4171/RMI/782