GRAFAKOS, Loukas; MAATI OUHABAZ, El

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GRAFAKOS, Loukas
Department of Mathematics, University of Missouri

MAATI OUHABAZ, El
Institut de Mathématiques de Bordeaux [IMB]

Langue

Document de travail - Pré-publication

Résumé en anglais

Let (X j , d j , µ j), j = 0, 1,. .. , m be metric measure spaces. Given 0 < p κ ≤ ∞ for κ = 1,. .. , m and an analytic family of multilinear operators T z : L p 1 (X 1) × • • • L p m (X m) → L 1 loc (X 0), for z in the complex unit strip, we prove a theorem in the spirit of Stein's complex interpolation for analytic families. Analyticity and our admissibility condition are defined in the weak (integral) sense and relax the pointwise definitions given in [9]. Continuous functions with compact support are natural dense subspaces of Lebesgue spaces over metric measure spaces and we assume the operators T z are initially defined on them. Our main lemma concerns the approximation of continuous functions with compact support by similar functions that depend analytically in an auxiliary parameter z. An application of the main theorem concerning bilinear estimates for Schrödinger operators on L p is included.< Réduire

Mots clés en anglais

multilinear operators

analytic families of operators

interpolation

bilinear estimates for Schrödinger operators

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191280

Project ANR

Analyse Réelle et Géométrie - ANR-18-CE40-0012

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251