Weighted norm inequalities for spectral multipliers without Gaussian estimates

The Anh Bui

doi:10.3836/tjm/1422452798

Weighted norm inequalities for spectral multipliers without Gaussian estimates

The Anh Bui^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Let L be a nonnegative self-adjoint operator on L²(Rⁿ) satisfying the full off-diagonal estimates L^q0 - L² for some q0 ∈ (1,2). In this paper, we study the sharp weighted L^p estimates for the spectral multipliers of the operator L and their commutators with BMO functions b. As an application, we study the weighted norm inequalities for spectral multipliers of Schrödinger operators with negative potentials.

Original language	English
Pages (from-to)	373-384
Number of pages	12
Journal	Tokyo Journal of Mathematics
Volume	37
Issue number	2
DOIs	https://doi.org/10.3836/tjm/1422452798
Publication status	Published - 1 Dec 2014

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title = "Weighted norm inequalities for spectral multipliers without Gaussian estimates",

abstract = "Let L be a nonnegative self-adjoint operator on L2(Rn) satisfying the full off-diagonal estimates Lq0 - L2 for some q0 ∈ (1,2). In this paper, we study the sharp weighted Lp estimates for the spectral multipliers of the operator L and their commutators with BMO functions b. As an application, we study the weighted norm inequalities for spectral multipliers of Schr{\"o}dinger operators with negative potentials.",

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AB - Let L be a nonnegative self-adjoint operator on L2(Rn) satisfying the full off-diagonal estimates Lq0 - L2 for some q0 ∈ (1,2). In this paper, we study the sharp weighted Lp estimates for the spectral multipliers of the operator L and their commutators with BMO functions b. As an application, we study the weighted norm inequalities for spectral multipliers of Schrödinger operators with negative potentials.

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Weighted norm inequalities for spectral multipliers without Gaussian estimates

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