Partial spectral multipliers and partial Riesz transforms for degenerate operators
| hal.structure.identifier | University of Auckland [Auckland] | |
| dc.contributor.author | A.F.M. TER ELST, . | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | OUHABAZ, El Maati | |
| dc.date.accessioned | 2024-04-04T02:18:07Z | |
| dc.date.available | 2024-04-04T02:18:07Z | |
| dc.date.created | 2013 | |
| dc.date.issued | 2013 | |
| dc.identifier.issn | 0213-2230 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189284 | |
| dc.description.abstractEn | We consider degenerate differential operators of the type A = − d k,j=1 ∂k(akj∂j) on L2(Rd) with real symmetric bounded measurable coefficients. Given a function χ ∈ C ∞ b (Rd) (respectively, a bounded Lipschitz domain Ω), suppose that (akj) ≥ μ > 0 a.e. on supp χ (respectively, a.e. on Ω). We prove a spectral multiplier type result: if F : [0,∞) → C is such that supt>0 ϕ(.)F(t.) Cs < ∞ for some nontrivial function ϕ ∈ C ∞ c (0,∞) and some s > d/2 then MχF(I + A)Mχ is weak type (1, 1) (respectively, PΩF(I +A)PΩ is weak type (1, 1)). We also prove boundedness on Lp for all p ∈ (1, 2] of the partial Riesz transforms Mχ∇(I + A) −1/2Mχ. The proofs are based on a criterion for a singular integral operator to be weak type (1, 1). | |
| dc.language.iso | en | |
| dc.publisher | European Mathematical Society | |
| dc.subject.en | Riesz transforms | |
| dc.subject.en | Spectral multipliers | |
| dc.subject.en | Gaussian bounds | |
| dc.subject.en | Gaussian bounds. | |
| dc.subject.en | singular integral operators | |
| dc.subject.en | degenerate operators | |
| dc.title.en | Partial spectral multipliers and partial Riesz transforms for degenerate operators | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.4171/rmi/735 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| bordeaux.journal | Revista Matemática Iberoamericana | |
| bordeaux.page | 691-713 | |
| bordeaux.volume | 29 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 2 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00992204 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00992204v1 | |
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