Estimates for cone multipliers associated with homogeneous functions

Sunggeum Hong; Joonil Kim; Chan Woo Yang

doi:10.1216/RMJ-2009-39-1-117

Estimates for cone multipliers associated with homogeneous functions

Sunggeum Hong, Joonil Kim, Chan Woo Yang

Department of Mathematics

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

Abstract

Let p C^∞(Rⁿ \ {0}) be homogeneous of degree one. We show that the convolution operator Tδf̂(ξ', ξ_n+1)=(1-p(ξ')/|ξ_n+1|)^δ f̂(ξ',ξ_n+1), (ξ',ξ_n+1 R ⁿ×R¹ is bounded from Hardy spaces H ^p(Rⁿ⁺¹) to L^P(Rⁿ⁺¹) for δ > n(l/p - 1/2) - 1/2, 0 < p < 1.

Original language	English
Pages (from-to)	117-132
Number of pages	16
Journal	Rocky Mountain Journal of Mathematics
Volume	39
Issue number	1
DOIs	https://doi.org/10.1216/RMJ-2009-39-1-117
Publication status	Published - 2009

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1216/RMJ-2009-39-1-117

Cite this

@article{9f13033ec52d45bbb56b79709d7bdd2b,

title = "Estimates for cone multipliers associated with homogeneous functions",

abstract = "Let p C∞(Rn \ {0}) be homogeneous of degree one. We show that the convolution operator Tδ{\^f}(ξ', ξn+1)=(1-p(ξ')/|ξn+1|)δ {\^f}(ξ',ξn+1), (ξ',ξn+1 R n×R1 is bounded from Hardy spaces H p(Rn+1) to LP(Rn+1) for δ > n(l/p - 1/2) - 1/2, 0 < p < 1.",

author = "Sunggeum Hong and Joonil Kim and Yang, {Chan Woo}",

year = "2009",

doi = "10.1216/RMJ-2009-39-1-117",

language = "English",

volume = "39",

pages = "117--132",

journal = "Rocky Mountain Journal of Mathematics",

issn = "0035-7596",

publisher = "Rocky Mountain Mathematics Consortium",

number = "1",

}

TY - JOUR

T1 - Estimates for cone multipliers associated with homogeneous functions

AU - Hong, Sunggeum

AU - Kim, Joonil

AU - Yang, Chan Woo

PY - 2009

Y1 - 2009

N2 - Let p C∞(Rn \ {0}) be homogeneous of degree one. We show that the convolution operator Tδf̂(ξ', ξn+1)=(1-p(ξ')/|ξn+1|)δ f̂(ξ',ξn+1), (ξ',ξn+1 R n×R1 is bounded from Hardy spaces H p(Rn+1) to LP(Rn+1) for δ > n(l/p - 1/2) - 1/2, 0 < p < 1.

AB - Let p C∞(Rn \ {0}) be homogeneous of degree one. We show that the convolution operator Tδf̂(ξ', ξn+1)=(1-p(ξ')/|ξn+1|)δ f̂(ξ',ξn+1), (ξ',ξn+1 R n×R1 is bounded from Hardy spaces H p(Rn+1) to LP(Rn+1) for δ > n(l/p - 1/2) - 1/2, 0 < p < 1.

UR - http://www.scopus.com/inward/record.url?scp=64849107838&partnerID=8YFLogxK

U2 - 10.1216/RMJ-2009-39-1-117

DO - 10.1216/RMJ-2009-39-1-117

M3 - Article

AN - SCOPUS:64849107838

SN - 0035-7596

VL - 39

SP - 117

EP - 132

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

IS - 1

ER -

Estimates for cone multipliers associated with homogeneous functions

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this