Littlewood-Paley-Stein functionals: an R-boundedness approach
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | COMETX, Thomas | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MAATI OUHABAZ, El | |
| dc.date.accessioned | 2024-04-04T02:37:31Z | |
| dc.date.available | 2024-04-04T02:37:31Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190802 | |
| dc.description.abstractEn | Let L = ∆ + V be a Schrödinger operator with a non-negative potential V on a complete Riemannian manifold M. We prove that the vertical Littlewwod-Paley-Stein functional associated with L is bounded on L p (M) if and only if the set { √ t ∇e −tL , t > 0} is R-bounded on L p (M). We also introduce and study more general functionals. For a sequence of functions m k : [0, ∞) → C, we define H((f k)) := ( \sum_k \int_0^\infty |∇m k (tL)f _k |^2 dt )^1/2 + (\sum_k \int_0^\infty | √ V m k (tL)f _k | 2 dt )^1/2. Under fairly reasonable assumptions on M we prove for certain functions m k the boundedness of H on L p (M) in the sense \| H((f _k)) \|_p ≤ C \| (\sum_k |f _k | 2 )^1/2 \|_p for some constant C independent of (f _k) _k. A lower estimate is also proved on the dual space L p. We introduce and study boundedness of other Littlewood-Paley-Stein type functionals and discuss their relationships to the Riesz transform. Several examples are given in the paper. | |
| dc.description.sponsorship | Analyse Réelle et Géométrie - ANR-18-CE40-0012 | |
| dc.language.iso | en | |
| dc.subject.en | Littlewood-Paley-Stein functionals | |
| dc.subject.en | Riesz transforms | |
| dc.subject.en | Kahane-Khintchin in- equality | |
| dc.subject.en | spectral multipliers | |
| dc.subject.en | Schrödinger operators | |
| dc.subject.en | elliptic operators | |
| dc.title.en | Littlewood-Paley-Stein functionals: an R-boundedness approach | |
| 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 | 2007.00284 | |
| 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-02884723 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02884723v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=COMETX,%20Thomas&MAATI%20OUHABAZ,%20El&rft.genre=preprint |
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