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Interpolation for analytic families of multilinear operators on metric measure spaces
| hal.structure.identifier | Department of Mathematics, University of Missouri | |
| dc.contributor.author | GRAFAKOS, Loukas | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MAATI OUHABAZ, El | |
| dc.date.accessioned | 2024-04-04T02:42:50Z | |
| dc.date.available | 2024-04-04T02:42:50Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191280 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Analyse Réelle et Géométrie - ANR-18-CE40-0012 | |
| dc.language.iso | en | |
| dc.subject.en | multilinear operators | |
| dc.subject.en | analytic families of operators | |
| dc.subject.en | interpolation | |
| dc.subject.en | bilinear estimates for Schrödinger operators | |
| dc.title.en | Interpolation for analytic families of multilinear operators on metric measure spaces | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 2107.00290 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03274470 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03274470v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=GRAFAKOS,%20Loukas&MAATI%20OUHABAZ,%20El&rft.genre=preprint |
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