The system will be going down for regular maintenance. Please save your work and logout.
Partial spectral multipliers and partial Riesz transforms for degenerate operators
Language
en
Article de revue
This item was published in
Revista Matemática Iberoamericana. 2013, vol. 29, n° 2, p. 691-713
European Mathematical Society
English Abstract
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), ...Read more >
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).Read less <
English Keywords
Riesz transforms
Spectral multipliers
Gaussian bounds
Gaussian bounds.
singular integral operators
degenerate operators
Origin
Hal imported