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Abstract
We prove a multiplier theorem of MihlinHörmandertype for operators of the form Δx–V(x) Δ_{y} on ℝ^{d1}_{x} ×ℝ^{d2}_{y }, where V(x) = ∑^{d1} _{j=1} V_{j}(x_{j}) the V_{j} are perturbations of the power law t ⟼t^{2σ} , and σ∈(1/2, ∞). The result is sharp whenever d_{1} ≥ σd_{2. }The main novelty of the result resides in its robustness: this appears to be the first sharp multiplier theorem for nonelliptic subelliptic operators allowing for step higher than two and perturbation of the coefficients. The proof hinges on precise estimates for eigenvalues and eigenfunctions of onedimensional Schrödinger operators, which are stable under perturbations of the potential.
Original language  English 

Pages (fromto)  75337574 
Number of pages  42 
Journal  Transactions of the American Mathematical Society 
Volume  373 
Issue number  11 
Early online date  9 Sep 2020 
DOIs  
Publication status  Published  Nov 2020 
Keywords
 BochnerRiesz mean
 Grushin operator
 Schrödinger operator
 Spectral multiplier
ASJC Scopus subject areas
 Mathematics(all)
 Applied Mathematics
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Dive into the research topics of 'A robust approach to sharp multiplier theorems for Grushin operators'. Together they form a unique fingerprint.Projects
 1 Finished

SubElliptic Harmonic Analysis
ENGINEERING & PHYSICAL SCIENCE RESEARCH COUNCIL
1/01/17 → 31/12/18
Project: Research Councils