TY - JOUR
T1 - Full range boundedness of bilinear hilbert transform along certain polynomials
AU - Dong, Dong
N1 - Funding Information:
This research is supported by LTS grant DO 0052. The author would also like to thank Prof. Xiaochun Li for helpful discussions on related topics.
Publisher Copyright:
© 2019 Element D.O.O. All Rights Reserved.
PY - 2019/1
Y1 - 2019/1
N2 - Let P and Q be two polynomials without constant term. Assume that the operator B P,Q ( f ,g)(x) = f (x-P(t))g(x-Q(t)) dt /t is bounded from L p1 ×L p2 into L r , p1, p2 ∈ (1,∞), 1/ p1 + 1/ p2 = 1/r . It is proved that if P′ (t) > 0 for all t ≠= 0, then r ≥ d/ d+1 . Here d is the correlation degree of P and Q which is defined as the largest multiplicity of non-zero real roots of P′ -Q′.
AB - Let P and Q be two polynomials without constant term. Assume that the operator B P,Q ( f ,g)(x) = f (x-P(t))g(x-Q(t)) dt /t is bounded from L p1 ×L p2 into L r , p1, p2 ∈ (1,∞), 1/ p1 + 1/ p2 = 1/r . It is proved that if P′ (t) > 0 for all t ≠= 0, then r ≥ d/ d+1 . Here d is the correlation degree of P and Q which is defined as the largest multiplicity of non-zero real roots of P′ -Q′.
KW - Bilinear hilbert transform
KW - Boundedness
KW - Correlation degree
KW - Full range
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U2 - 10.7153/mia-2019-22-11
DO - 10.7153/mia-2019-22-11
M3 - Article
AN - SCOPUS:85062645794
SN - 1331-4343
VL - 22
SP - 151
EP - 156
JO - Mathematical Inequalities and Applications
JF - Mathematical Inequalities and Applications
ER -