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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U2 - 10.1007/s00020-009-1731-9
DO - 10.1007/s00020-009-1731-9
M3 - Article
AN - SCOPUS:76449112960
VL - 65
SP - 485
EP - 528
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
SN - 0378-620X
IS - 4
ER -