A local-to-global boundedness argument and Fourier integral operators

被引：15

作者：

Ruzhansky, Michael ^{[1
,3
,4
]}

Sugimoto, Mitsuru ^{[2
]}

机构：

[1] Imperial Coll London, Dept Math, 180 Queens Gate, London SW7 2AZ, England

[2] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

[3] Univ Ghent, Dept Math Anal Log & Discrete Math, Ghent, Belgium

[4] Queen Mary Univ London, Sch Math Sci, London, England

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 473卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

Integral operators; L-P-boundedness; Fourier integral operators; REGULARITY; EQUATIONS; SPACES;

D O I：

10.1016/j.jmaa.2018.12.074

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a criterion for the global boundedness of integral operators which are known to be locally bounded. As an application, we discuss the global L-P-boundedness for a class of Fourier integral operators. While the local L-P-boundedness of Fourier integral operators is known from the work of Seeger, Sogge and Stein [26], not so many results are available for the global boundedness on L-P(R-n). We give several natural sufficient conditions for them. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：892 / 904

页数：13

共 30 条

[1]

[Anonymous], 1970, SINGULAR INTEGRALS D

[2]

Asada K., 1978, JPN J MATH NS, V4, P299

[3]

Beals M., 1982, MEM AM MATH SOC, V38

[4] EXTENSIONS OF HARDY SPACES AND THEIR USE IN ANALYSIS [J].

COIFMAN, RR ;

WEISS, G .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 83 (04) :569-645

[5] GLOBAL Lp CONTINUITY OF FOURIER INTEGRAL OPERATORS [J].

Coriasco, Sandro ;

Ruzhansky, Michael .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 366 (05) :2575-2596

[6] On the boundedness of Fourier integral operators on Lp(Rn) [J].

Coriasco, Sandro ;

Ruzhansky, Michael .

COMPTES RENDUS MATHEMATIQUE, 2010, 348 (15-16) :847-851

[7]

Dos Santos Ferreira D, 2014, MEM AM MATH SOC, V229, P1074

[8]

Duistermaat J. J., 1996, PROGR MATH, V130

[9]

Eskin G. I., 1970, MAT SBORNIK, V82, P585

[10]

FEFFERMAN C, 1972, ACTA MATH-UPPSALA, V129, P137, DOI 10.1007/BF02392215

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