We prove the Lp-differentiability at almost every point for convolution products on ℝd of the form K*μ, where μ is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation.
On the Lp-differentiability of certain classes of functions / Alberti, G.; Bianchini, S.; Crippa, G.. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - 30:1(2014), pp. 349-367. [10.4171/rmi/782]
On the Lp-differentiability of certain classes of functions
Bianchini S.;
2014-01-01
Abstract
We prove the Lp-differentiability at almost every point for convolution products on ℝd of the form K*μ, where μ is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation.File in questo prodotto:
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