L^p-integrability of the second order derivatives of Green potentials in convex domains

Vilhelm Adolfsson

Vol. 159 (1993), No. 2, 201–225

DOI: 10.2140/pjm.1993.159.201

Abstract

We give estimates in L^P, 1 < p ≤ 2, of the second order derivatives of the Green potential of f ∈ L^p, for convex domains. This is done by interpolating between estimates in L¹ and L² of functions in atomic H¹ and L², respectively. The crucial step is obtaining the atomic estimate which is done by adapting to the present situation, a technique introduced by Dahlberg and Kenig.

Mathematical Subject Classification 2000

Primary: 35B45

Secondary: 35J05

Milestones

Received: 26 September 1991

Published: 1 June 1993