JournalsrmiVol. 30, No. 1pp. 349–367

On the LpL^p-differentiability of certain classes of functions

  • Giovanni Alberti

    Università di Pisa, Italy
  • Stefano Bianchini

    SISSA-ISAS, Trieste, Italy
  • Gianluca Crippa

    Universität Basel, Switzerland
On the $L^p$-differentiability  of certain classes of functions cover
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Abstract

We prove the LpL^p-differentiability at almost every point for convolution products on Rd\mathbb{R}^d of the form KμK*\mu, where μ\mu is bounded measure and KK is a homogeneous kernel of degree 1d1-d. From this result we derive the LpL^p-differentiability for vector fields on Rd\mathbb{R}^d 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 LpL^p-differentiability of certain classes of functions. Rev. Mat. Iberoam. 30 (2014), no. 1, pp. 349–367

DOI 10.4171/RMI/782