BILINEAR HILBERT TRANSFORMS ALONG CURVES I: THE MONOMIAL CASE

被引：34

作者：

Li, Xiaochun ^{[1
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

ANALYSIS & PDE | 2013年 / 6卷 / 01期

关键词：

bilinear Hilbert transform along curves; OSCILLATORY INTEGRALS;

D O I：

10.2140/apde.2013.6.197

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish an L-2 x L-2 to L-1 estimate for the bilinear Hilbert transform along a curve defined by a monomial. Our proof is closely related to multilinear oscillatory integrals.

引用

页码：197 / 220

页数：24

共 19 条

[1] Multidimensional van der Corput and sublevel set estimates [J].

Carbery, A ;

Christ, M ;

Wright, J .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 12 (04) :981-1015

[2]

Christ M, 2005, DUKE MATH J, V130, P321

[3] HILBERT-TRANSFORMS ALONG CURVES .1. NILPOTENT GROUPS [J].

CHRIST, M .

ANNALS OF MATHEMATICS, 1985, 122 (03) :575-596

[4] Singular and maximal Radon transforms: Analysis and geometry [J].

Christ, M ;

Nagel, A ;

Stein, EM ;

Wainger, S .

ANNALS OF MATHEMATICS, 1999, 150 (02) :489-577

[5] HILBERT-TRANSFORMS ALONG CURVES .2. A FLAT CASE [J].

CHRIST, M .

DUKE MATHEMATICAL JOURNAL, 1985, 52 (04) :887-894

[6] MAXIMAL AND SINGULAR INTEGRAL-OPERATORS VIA FOURIER-TRANSFORM ESTIMATES [J].

DUOANDIKOETXEA, J ;

DEFRANCIA, JLR .

INVENTIONES MATHEMATICAE, 1986, 84 (03) :541-561

[7] SINGULAR INTEGRALS WITH MIXED HOMOGENEITY [J].

FABES, EB ;

RIVIERE, NM .

STUDIA MATHEMATICA, 1966, 27 (01) :19-&

[8]

Furstenberg H., 1990, The legacy of John von Neumann, V50, P43

[9] A new proof of Szemeredi's theorem for arithmetic progressions of length four [J].

Gowers, WT .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 1998, 8 (03) :529-551

[10] OSCILLATORY INTEGRALS AND MULTIPLIERS ON FLP [J].

HORMANDER, L .

ARKIV FOR MATEMATIK, 1973, 11 (01) :1-11

← 1 2 →