Imaginary powers of Laplace operators

Sikora, Adam; Wright, James

doi:10.1090/s0002-9939-00-05754-3

Cited by 58 publications

(37 citation statements)

References 20 publications

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“…Since the kernels of e −t(1+Hc) and e −t(1−∆) obey the Gaussian upper bound as in (2.21), we have by Sikora-Wright [37] that…”

Section: Andmentioning

confidence: 96%

On nonlinear Schrödinger equations with repulsive inverse-power potentials

Dinh¹

2018

Preprint

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In this paper, we consider the Cauchy problem for the nonlinear Schrödinger equations with repulsive inverse-power potentialsWe study the local and global well-posedness, finite time blow-up and scattering in the energy space H 1 for the equation. These results extend a recent work of Miao-Zhang-Zheng [Nonlinear Schrödinger equation with coulomb potential, arXiv:1809.06685] to a general class of inverse-power potentials and higher dimensions.

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“…Since the kernels of e −t(1+Hc) and e −t(1−∆) obey the Gaussian upper bound as in (2.21), we have by Sikora-Wright [37] that…”

Section: Andmentioning

confidence: 96%

On nonlinear Schrödinger equations with repulsive inverse-power potentials

Dinh¹

2018

Preprint

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“…The smoothness condition s > n/2 in these results is sharp, in the sense that n/2 cannot be replaced by a smaller quantity (see, e.g., [SW01] and references therein). In addition, the validity of these results has little to do with the symmetries of the Euclidean Laplace operator (such as homogeneity and translation-invariance): indeed analogous sharp results can be obtained in the case where L is an elliptic selfadjoint (pseudo)differential operator on a compact manifold [SS89].…”

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confidence: 88%

A robust approach to sharp multiplier theorems for Grushin operators

Dall’Ara

Martini

2020

Trans. Amer. Math. Soc.

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“…where s = log 2 C d . This can be checked by a careful proof reading of [53,Theorem 1]. Also a stronger result can be found in [24].…”

Section: Complex Interpolationmentioning

confidence: 87%