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 › peer-review

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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title = "Triple Hilbert transforms along polynomial surfaces",

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} Ωam tm is bounded in Lp(ℝ4).",

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

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

note = "Funding Information: The third author was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korean government (MOST) (R01-2007-000-10527-0) and the fourth author was supported by the Korea Research Foundation grant funded by the Korean government (KRF-2008-331-C00016).",

year = "2009",

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doi = "10.1007/s00020-009-1731-9",

language = "English",

volume = "65",

pages = "485--528",

journal = "Integral Equations and Operator Theory",

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TY - JOUR

T1 - Triple Hilbert transforms along polynomial surfaces

AU - Cho, Yong Kum

AU - Hong, Sunggeum

AU - Kim, Joonil

AU - Yang, Chan Woo

N1 - Funding Information: The third author was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korean government (MOST) (R01-2007-000-10527-0) and the fourth author was supported by the Korea Research Foundation grant funded by the Korean government (KRF-2008-331-C00016).

PY - 2009/12

Y1 - 2009/12

N2 - 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} Ωam tm is bounded in Lp(ℝ4).

AB - 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} Ωam tm is bounded in Lp(ℝ4).

KW - Even in column

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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VL - 65

SP - 485

EP - 528

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

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