COMETX, Thomas; MAATI OUHABAZ, El

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COMETX, Thomas
Institut de Mathématiques de Bordeaux [IMB]

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

Idioma

Document de travail - Pré-publication

Resumen en inglés

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.< Leer menos

Palabras clave en inglés

Littlewood-Paley-Stein functionals

Riesz transforms

Kahane-Khintchin in- equality

spectral multipliers

Schrödinger operators

elliptic operators

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190802

Proyecto ANR

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

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251