On radial and conical Fourier multipliers

Yaryong Heo; Fëdor Nazarov; Andreas Seeger

doi:10.1007/s12220-010-9171-y

On radial and conical Fourier multipliers

Yaryong Heo, Fëdor Nazarov, Andreas Seeger

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

12 Citations (Scopus)

Abstract

We investigate connections between radial Fourier multipliers on ℝ^d and certain conical Fourier multipliers on ℝ^d+1. As an application we obtain a new weak type endpoint bound for the Bochner-Riesz multipliers associated with the light cone in ℝ^d+1, where d≥4, and results on characterizations of L ^p →L^p,ν inequalities for convolutions with radial kernels.

Original language	English
Pages (from-to)	96-117
Number of pages	22
Journal	Journal of Geometric Analysis
Volume	21
Issue number	1
DOIs	https://doi.org/10.1007/s12220-010-9171-y
Publication status	Published - 2011 Jan
Externally published	Yes

Keywords

Cone multiplier
Radial Fourier multipliers
Weak type estimates

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s12220-010-9171-y

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title = "On radial and conical Fourier multipliers",

abstract = "We investigate connections between radial Fourier multipliers on ℝd and certain conical Fourier multipliers on ℝd+1. As an application we obtain a new weak type endpoint bound for the Bochner-Riesz multipliers associated with the light cone in ℝd+1, where d≥4, and results on characterizations of L p →Lp,ν inequalities for convolutions with radial kernels.",

keywords = "Cone multiplier, Radial Fourier multipliers, Weak type estimates",

author = "Yaryong Heo and F{\"e}dor Nazarov and Andreas Seeger",

note = "Funding Information: Y.H. supported by Korea Research Foundation Grant KRF-2008-357-C00002 and National Research Foundation of Korea Grant NRF-2009-0094068. F.N. supported in part by NSF grant 0800243. A.S. supported in part by NSF grant 0652890.",

year = "2011",

month = jan,

doi = "10.1007/s12220-010-9171-y",

language = "English",

volume = "21",

pages = "96--117",

journal = "Journal of Geometric Analysis",

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TY - JOUR

T1 - On radial and conical Fourier multipliers

AU - Heo, Yaryong

AU - Nazarov, Fëdor

AU - Seeger, Andreas

N1 - Funding Information: Y.H. supported by Korea Research Foundation Grant KRF-2008-357-C00002 and National Research Foundation of Korea Grant NRF-2009-0094068. F.N. supported in part by NSF grant 0800243. A.S. supported in part by NSF grant 0652890.

PY - 2011/1

Y1 - 2011/1

N2 - We investigate connections between radial Fourier multipliers on ℝd and certain conical Fourier multipliers on ℝd+1. As an application we obtain a new weak type endpoint bound for the Bochner-Riesz multipliers associated with the light cone in ℝd+1, where d≥4, and results on characterizations of L p →Lp,ν inequalities for convolutions with radial kernels.

AB - We investigate connections between radial Fourier multipliers on ℝd and certain conical Fourier multipliers on ℝd+1. As an application we obtain a new weak type endpoint bound for the Bochner-Riesz multipliers associated with the light cone in ℝd+1, where d≥4, and results on characterizations of L p →Lp,ν inequalities for convolutions with radial kernels.

KW - Cone multiplier

KW - Radial Fourier multipliers

KW - Weak type estimates

UR - http://www.scopus.com/inward/record.url?scp=79951508807&partnerID=8YFLogxK

U2 - 10.1007/s12220-010-9171-y

DO - 10.1007/s12220-010-9171-y

M3 - Article

AN - SCOPUS:79951508807

SN - 1050-6926

VL - 21

SP - 96

EP - 117

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 1

ER -

On radial and conical Fourier multipliers

Abstract

Keywords

ASJC Scopus subject areas

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