Triple Hilbert transforms along polynomial surfaces

Yong Kum Cho; Sunggeum Hong; Joonil Kim; Chan Woo Yang

doi:10.1007/s00020-009-1731-9

Triple Hilbert transforms along polynomial surfaces

Yong Kum Cho, Sunggeum Hong, Joonil Kim, Chan Woo Yang

Department of Mathematics

Research output: Contribution to journal › Article

3 Citations (Scopus)

Abstract

Given Ω ⊂ ℤ₊³, we discuss a necessary and sufficient condition that the triple Hilbert transform associated with any polynomial of the form (t₁,t₂,t₃, ∑_{m Ie{cyrillic, ukrainian} Ω}a_m t^m is bounded in L^p(ℝ⁴).

Original language	English
Pages (from-to)	485-528
Number of pages	44
Journal	Integral Equations and Operator Theory
Volume	65
Issue number	4
DOIs	https://doi.org/10.1007/s00020-009-1731-9
Publication status	Published - 2009 Dec

Keywords

Even in column
Littlewood-Paley operator
Newton polyhedron
Oscillatory singular integral
Triple Hilbert transform
Van der Corput's lemma

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-009-1731-9

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Cho, Y. K., Hong, S., Kim, J., & Yang, C. W. (2009). Triple Hilbert transforms along polynomial surfaces. Integral Equations and Operator Theory, 65(4), 485-528. https://doi.org/10.1007/s00020-009-1731-9

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keywords = "Even in column, Littlewood-Paley operator, Newton polyhedron, Oscillatory singular integral, Triple Hilbert transform, Van der Corput's lemma",

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AU - Cho, Yong Kum

AU - Hong, Sunggeum

AU - Kim, Joonil

AU - Yang, Chan Woo

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KW - Littlewood-Paley operator

KW - Newton polyhedron

KW - Oscillatory singular integral

KW - Triple Hilbert transform

KW - Van der Corput's lemma

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