On L2-Boundedness of h-Pseudodifferential Operators

被引：1

作者：

Yang, Jie ^{[1
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Xinjiang 830046, Peoples R China

来源：

JOURNAL OF FUNCTION SPACES | 2021年 / 2021卷

基金：

中国国家自然科学基金;

关键词：

D O I：

10.1155/2021/6690963

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let T-a(h) be the h-pseudodifferential operators with symbol a. When a is an element of S-rho,1(m) and m = n(rho - 1)/2, it is well known that T-a(h) is not always bounded in L-2(R-n). In this paper, under the condition a(x, xi) is an element of L-infinity S-rho(n) (rho-1)/2 (omega), we show that T-a(h) is bounded on L-2.

引用

页数：5

共 18 条

[1] The boundedness of h-admissible Fourier integral operators on Bessel potential spaces [J].

Aid, Omar Farouk ;

Senoussaoui, Abderrahmane .

TURKISH JOURNAL OF MATHEMATICS, 2019, 43 (05) :2125-2141

[2] On the global LP boundedness of a general class of h-Fourier integral operators [J].

Aitemrar, Chafika Amel ;

Senoussaoui, Abderrahmane .

TURKISH JOURNAL OF MATHEMATICS, 2018, 42 (04) :1726-1737

[3] h-Admissible Fourier integral operators [J].

Aitemrar, Chafika Amel ;

Senoussaoui, Abderrahmane .

TURKISH JOURNAL OF MATHEMATICS, 2016, 40 (03) :553-568

[4] Global h Fourier integral operators with complex-valued phase functions [J].

Butler, J .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2002, 34 :479-489

[5] PSEUDODIFFERENTIAL OPERATORS WITH NONREGULAR SYMBOLS [J].

CHING, CH .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1972, 11 (02) :436-&

[6] ON A CLASS OF h-FOURIER INTEGRAL OPERATORS [J].

Harrat, Chahrazed ;

Senoussaoui, Abderrahmane .

DEMONSTRATIO MATHEMATICA, 2014, 47 (03) :595-606

[7]

HELFFER B, 1981, ANN I FOURIER, V31, P169

[8] FUNCTIONAL CALCULATION BY THE MELLIN TRANSFORMATION AND ADMISSIBLE OPERATORS [J].

HELFFER, B ;

ROBERT, D .

JOURNAL OF FUNCTIONAL ANALYSIS, 1983, 53 (03) :246-268

[9]

Helffer B, 1984, AST RISQUE, V112

[10] ON THE L2-BOUNDEDNESS OF PSEUDODIFFERENTIAL-OPERATORS [J].

HIGUCHI, Y ;

NAGASE, M .

JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1988, 28 (01) :133-139

← 1 2 →