Weighted spectral cluster bounds and a sharp multiplier theorem for ultraspherical Grushin operators

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Weighted spectral cluster bounds and a sharp multiplier theorem for ultraspherical Grushin operators. / Casarino, Valentina; Ciatti, Paolo; Martini, Alessio.

In: International Mathematics Research Notices, 10.03.2021.

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@article{97fdcf19c0cc4f31a8a2da924bec2ba1,
title = "Weighted spectral cluster bounds and a sharp multiplier theorem for ultraspherical Grushin operators",
abstract = "We study degenerate elliptic operators of Grushin type on the d-dimensional sphere, which are singular on a k-dimensional sphere for some k<d⁠. For these operators we prove a spectral multiplier theorem of Mihlin–H{\"o}rmander type, which is optimal whenever 2k≤d⁠, and a corresponding Bochner–Riesz summability result. The proof hinges on suitable weighted spectral cluster bounds, which in turn depend on precise estimates for ultraspherical polynomials.",
author = "Valentina Casarino and Paolo Ciatti and Alessio Martini",
year = "2021",
month = mar,
day = "10",
doi = "10.1093/imrn/rnab007",
language = "English",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",

}

RIS

TY - JOUR

T1 - Weighted spectral cluster bounds and a sharp multiplier theorem for ultraspherical Grushin operators

AU - Casarino, Valentina

AU - Ciatti, Paolo

AU - Martini, Alessio

PY - 2021/3/10

Y1 - 2021/3/10

N2 - We study degenerate elliptic operators of Grushin type on the d-dimensional sphere, which are singular on a k-dimensional sphere for some k<d⁠. For these operators we prove a spectral multiplier theorem of Mihlin–Hörmander type, which is optimal whenever 2k≤d⁠, and a corresponding Bochner–Riesz summability result. The proof hinges on suitable weighted spectral cluster bounds, which in turn depend on precise estimates for ultraspherical polynomials.

AB - We study degenerate elliptic operators of Grushin type on the d-dimensional sphere, which are singular on a k-dimensional sphere for some k<d⁠. For these operators we prove a spectral multiplier theorem of Mihlin–Hörmander type, which is optimal whenever 2k≤d⁠, and a corresponding Bochner–Riesz summability result. The proof hinges on suitable weighted spectral cluster bounds, which in turn depend on precise estimates for ultraspherical polynomials.

UR - https://academic.oup.com/imrn

U2 - 10.1093/imrn/rnab007

DO - 10.1093/imrn/rnab007

M3 - Article

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

ER -