BOUNDEDNESS OF FOURIER INTEGRAL OPERATORS ON FLp SPACES

被引：37

作者：

Cordero, Elena ^{[1
]}

Nicola, Fabio ^{[2
]}

Rodino, Luigi ^{[1
]}

机构：

[1] Univ Turin, Dept Math, I-10123 Turin, Italy

[2] Politecn Torino, Dipartimento Matemat, I-10129 Turin, Italy

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 361卷 / 11期

关键词：

Fourier Integral Operators; FLp spaces; Beurling-Helson's theorem; modulation spaces; short-time Fourier transform; MODULATION SPACES;

D O I：

10.1090/S0002-9947-09-04848-X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the action of Fourier Integral Operators (FIOs) of Hormander's type on FLp (R-d)(comp), 1 <= p <= infinity We see, from the Beurling-Helson theorem, that generally FIOs of order zero fail to be bounded oil these spaces when p not equal 2, the counterexample being given by any smooth non-linear change of variable Here we show that FIOs of order m = -d vertical bar 1/2 - 1/p vertical bar are instead bounded. Moreover, this loss of derivatives is proved to be sharp ill every dimension d >= 1, even for phases which are linear in the dual variables The proofs make use of tools from time-frequency analysis such as the theory of modulation spaces

引用

页码：6049 / 6071

页数：23

共 26 条

[1] Unimodular Fourier multipliers for modulation spaces [J].