scholarly journals Restriction and spectral multiplier theorems on asymptotically conic manifolds

2013 ◽  
Vol 6 (4) ◽  
pp. 893-950 ◽  
Author(s):  
Colin Guillarmou ◽  
Andrew Hassell ◽  
Adam Sikora
Keyword(s):  
Spectral Multiplier ◽  
Multiplier Theorems ◽  
Spectral Multiplier Theorems

scholarly journals Remarks on L p -limiting absorption principle of Schrödinger operators and applications to spectral multiplier theorems

2018 ◽  
Vol 30 (1) ◽  
pp. 43-55 ◽  
Author(s):  
Shanlin Huang ◽  
Xiaohua Yao ◽  
Quan Zheng
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Spectral Condition ◽  
Multiplier Theorem ◽  
Spectral Multiplier ◽  
Limiting Absorption Principle ◽  
Riesz Operators ◽  
Multiplier Theorems ◽  
Spectral Multiplier Theorems ◽  
Formula Type

Abstract This paper comprises two parts. We first investigate an {L^{p}} -type of limiting absorption principle for Schrödinger operators {H=-\Delta+V} on {\mathbb{R}^{n}} ( {n\geq 3} ), i.e., we prove the ϵ-uniform {L^{{2(n+1)}/({n+3})}} – {L^{{2(n+1)}/({n-1})}} -estimates of the resolvent {(H-\lambda\pm i\epsilon)^{-1}} for all {\lambda>0} under the assumptions that the potential V belongs to some integrable spaces and a spectral condition of H at zero is satisfied. As applications, we establish a sharp Hörmander-type spectral multiplier theorem associated with Schrödinger operators H and deduce {L^{p}} -bounds of the corresponding Bochner–Riesz operators. Next, we consider the fractional Schrödinger operator {H=(-\Delta)^{\alpha}+V} ( {0<2\alpha<n} ) and prove a uniform Hardy–Littlewood–Sobolev inequality for {(-\Delta)^{\alpha}} , which generalizes the corresponding result of Kenig–Ruiz–Sogge [20].

scholarly journals Spectral multiplier theorems and averaged R-boundedness

2017 ◽  
Vol 94 (2) ◽  
pp. 260-296 ◽  
Author(s):  
Christoph Kriegler ◽  
Lutz Weis
Keyword(s):  
Spectral Multiplier ◽  
Multiplier Theorems ◽  
Spectral Multiplier Theorems

scholarly journals A robust approach to sharp multiplier theorems for Grushin operators

2020 ◽  
Vol 373 (11) ◽  
pp. 7533-7574
Author(s):  
Gian Maria Dall’Ara ◽  
Alessio Martini
Keyword(s):  
Robust Approach ◽  
Grushin Operators ◽  
Multiplier Theorems
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