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hal.structure.identifierDepartment of Mathematics, University of Missouri
dc.contributor.authorGRAFAKOS, Loukas
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMAATI OUHABAZ, El
dc.date.accessioned2024-04-04T02:42:50Z
dc.date.available2024-04-04T02:42:50Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191280
dc.description.abstractEnLet (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.
dc.description.sponsorshipAnalyse Réelle et Géométrie - ANR-18-CE40-0012
dc.language.isoen
dc.subject.enmultilinear operators
dc.subject.enanalytic families of operators
dc.subject.eninterpolation
dc.subject.enbilinear estimates for Schrödinger operators
dc.title.enInterpolation for analytic families of multilinear operators on metric measure spaces
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.identifier.arxiv2107.00290
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-03274470
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03274470v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.au=GRAFAKOS,%20Loukas&amp;MAATI%20OUHABAZ,%20El&amp;rft.genre=preprint


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