Transferring spherical multipliers on compact symmetric spaces

Sanjiv Kumar Gupta; Kathryn E. Hare

doi:10.1007/s00209-021-02694-x

Transferring spherical multipliers on compact symmetric spaces

Sanjiv Kumar Gupta^*, Kathryn E. Hare

^*Corresponding author for this work

Mathematics & Statistics

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

Abstract

We prove a two-sided transference theorem between L^p spherical multipliers on the compact symmetric space U/K and L^p multipliers on the vector space ip, where the Lie algebra of U has Cartan decomposition k⊕ ip. This generalizes the classic theorem transference theorem of deLeeuw relating multipliers on L^p(T) and L^p(R).

Original language	English
Pages (from-to)	883-897
Number of pages	15
Journal	Mathematische Zeitschrift
Volume	298
Issue number	1-2
DOIs	https://doi.org/10.1007/s00209-021-02694-x
Publication status	Published - Jun 2021

Keywords

Compact symmetric space
Spherical multiplier
Transference

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00209-021-02694-x

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title = "Transferring spherical multipliers on compact symmetric spaces",

abstract = "We prove a two-sided transference theorem between Lp spherical multipliers on the compact symmetric space U/K and Lp multipliers on the vector space ip, where the Lie algebra of U has Cartan decomposition k⊕ ip. This generalizes the classic theorem transference theorem of deLeeuw relating multipliers on Lp(T) and Lp(R).",

keywords = "Compact symmetric space, Spherical multiplier, Transference",

author = "Gupta, {Sanjiv Kumar} and Hare, {Kathryn E.}",

note = "Funding Information: This research is supported in part by NSERC 2016-03719 and by Sultan Qaboos University. The first author thanks the University of Waterloo for their hospitality when some of this research was done Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.",

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doi = "10.1007/s00209-021-02694-x",

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AU - Gupta, Sanjiv Kumar

AU - Hare, Kathryn E.

N1 - Funding Information: This research is supported in part by NSERC 2016-03719 and by Sultan Qaboos University. The first author thanks the University of Waterloo for their hospitality when some of this research was done Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.

PY - 2021/6

Y1 - 2021/6

N2 - We prove a two-sided transference theorem between Lp spherical multipliers on the compact symmetric space U/K and Lp multipliers on the vector space ip, where the Lie algebra of U has Cartan decomposition k⊕ ip. This generalizes the classic theorem transference theorem of deLeeuw relating multipliers on Lp(T) and Lp(R).

AB - We prove a two-sided transference theorem between Lp spherical multipliers on the compact symmetric space U/K and Lp multipliers on the vector space ip, where the Lie algebra of U has Cartan decomposition k⊕ ip. This generalizes the classic theorem transference theorem of deLeeuw relating multipliers on Lp(T) and Lp(R).

KW - Compact symmetric space

KW - Spherical multiplier

KW - Transference

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Transferring spherical multipliers on compact symmetric spaces

Abstract

Keywords

ASJC Scopus subject areas

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