Bochner-Riesz summability for analytic functions on the m-complex unit sphere and for cylindrically symmetric functions on ℝn-1 × ℝ

Adam Sikora; Terence Tao

doi:10.4310/CAG.2004.v12.n1.a4

Bochner-Riesz summability for analytic functions on the m-complex unit sphere and for cylindrically symmetric functions on ℝ^n-1 × ℝ

Adam Sikora^*, Terence Tao

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

We prove that spectral projections of Laplace-Beltrami operator on the m-complex unit sphere E_ΔS2m-1 ([0, R)) are uniformly bounded as operators from H^P(S^2m-1) to L^p(S ^2m-1) for all p ∈ (1, ∈). We also show that the Bochner-Riesz conjecture is true when restricted to cylindrically symmetric functions on ℝ^n-1 × ℝ.

Original language	English
Pages (from-to)	43-57
Number of pages	15
Journal	Communications in Analysis and Geometry
Volume	12
Issue number	1-2
DOIs	https://doi.org/10.4310/CAG.2004.v12.n1.a4
Publication status	Published - 2004
Externally published	Yes

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abstract = "We prove that spectral projections of Laplace-Beltrami operator on the m-complex unit sphere EΔS2m-1 ([0, R)) are uniformly bounded as operators from HP(S2m-1) to Lp(S 2m-1) for all p ∈ (1, ∈). We also show that the Bochner-Riesz conjecture is true when restricted to cylindrically symmetric functions on ℝn-1 × ℝ.",

author = "Adam Sikora and Terence Tao",

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doi = "10.4310/CAG.2004.v12.n1.a4",

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AU - Tao, Terence

PY - 2004

Y1 - 2004

N2 - We prove that spectral projections of Laplace-Beltrami operator on the m-complex unit sphere EΔS2m-1 ([0, R)) are uniformly bounded as operators from HP(S2m-1) to Lp(S 2m-1) for all p ∈ (1, ∈). We also show that the Bochner-Riesz conjecture is true when restricted to cylindrically symmetric functions on ℝn-1 × ℝ.

AB - We prove that spectral projections of Laplace-Beltrami operator on the m-complex unit sphere EΔS2m-1 ([0, R)) are uniformly bounded as operators from HP(S2m-1) to Lp(S 2m-1) for all p ∈ (1, ∈). We also show that the Bochner-Riesz conjecture is true when restricted to cylindrically symmetric functions on ℝn-1 × ℝ.

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DO - 10.4310/CAG.2004.v12.n1.a4

M3 - Article

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VL - 12

SP - 43

EP - 57

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

IS - 1-2

ER -

Bochner-Riesz summability for analytic functions on the m-complex unit sphere and for cylindrically symmetric functions on ℝ^n-1 × ℝ

Abstract

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