TY - JOUR
T1 - Spectral multipliers, Bochner–Riesz means and uniform Sobolev inequalities for elliptic operators
AU - Sikora, Adam
AU - Yan, Lixin
AU - Yao, Xiaohua
PY - 2018/5/18
Y1 - 2018/5/18
N2 - This article comprises two parts. In the first, we study Lp to Lq bounds for spectral multipliers and Bochner–Riesz means with negative index in the general setting of abstract self-adjoint operators. In the second, we obtain the uniform Sobolev estimates for constant coefficients higher order elliptic operators P(D)−z and all z∈ℂ∖[0,∞), which give an extension of the second order results of Kenig–Ruiz–Sogge [42]. Next we use perturbation techniques to prove the uniform Sobolev estimates for Schrödingier operators P(D)+V with small integrable potentials V. Finally, we deduce spectral multiplier applications for all these operators, including sharp Bochner–Riesz summability results.
AB - This article comprises two parts. In the first, we study Lp to Lq bounds for spectral multipliers and Bochner–Riesz means with negative index in the general setting of abstract self-adjoint operators. In the second, we obtain the uniform Sobolev estimates for constant coefficients higher order elliptic operators P(D)−z and all z∈ℂ∖[0,∞), which give an extension of the second order results of Kenig–Ruiz–Sogge [42]. Next we use perturbation techniques to prove the uniform Sobolev estimates for Schrödingier operators P(D)+V with small integrable potentials V. Finally, we deduce spectral multiplier applications for all these operators, including sharp Bochner–Riesz summability results.
UR - http://purl.org/au-research/grants/arc/DP130101302
UR - http://www.scopus.com/inward/record.url?scp=85043723365&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnw323
DO - 10.1093/imrn/rnw323
M3 - Article
VL - 2018
SP - 3070
EP - 3121
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 10
ER -