Singular integral operators with operator-valued kernels, and extrapolation of maximal regularity into rearrangement invariant Banach function spaces

Ralph Chill (1) , Alberto Fiorenza (2)

1 IECL - Institut Élie Cartan de Lorraine
2 University of Naples Federico II = Università degli studi di Napoli Federico II

We prove two extrapolation results for singular integral operators with operator-valued kernels and we apply these results in order to obtain the following extrapolation of L p-maximal regularity: if an autonomous Cauchy problem on a Banach space has L p-maximal regularity for some p ∈ (1, ∞), then it has E w-maximal regularity for every rearrangement-invariant Banach function space E with Boyd indices 1 < p E ≤ q E < ∞ and every Muckenhoupt weight w ∈ A p E. We prove a similar result for non-autonomous Cauchy problems on the line.

Domaines: Analyse fonctionnelle [math.FA]; Analyse classique [math.CA]

Ralph Chill, Alberto Fiorenza. Singular integral operators with operator-valued kernels, and extrapolation of maximal regularity into rearrangement invariant Banach function spaces. Journal of Evolution Equations, 2014, 14 (4), pp.795-828. ⟨10.1007/s00028-014-0239-1⟩. ⟨hal-01275671⟩