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

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

General Mathematics

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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.

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Estimates for cone multipliers associated with homogeneous functions

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