Please wait a minute...
Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

邮发代号 80-964

2019 Impact Factor: 1.03

Frontiers of Mathematics in China  2023, Vol. 18 Issue (4): 235-249   https://doi.org/10.3868/s140-DDD-023-0019-x
  本期目录
L1 Boundedness of a class of rough Fourier integral operators
Xiangrong ZHU, Yuchao MA()
School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China
 全文: PDF(527 KB)   HTML
Abstract

In this note, we consider a class of Fourier integral operators with rough amplitudes and rough phases. When the index of symbols in some range, we prove that they are bounded on L1 and construct an example to show that this result is sharp in some cases. This result is a generalization of the corresponding theorems of Kenig-Staubach and Dos Santos Ferreira-Staubach.

Key wordsFourier integral operators    amplitude    phase
出版日期: 2023-12-12
Corresponding Author(s): Yuchao MA   
 引用本文:   
. [J]. Frontiers of Mathematics in China, 2023, 18(4): 235-249.
Xiangrong ZHU, Yuchao MA. L1 Boundedness of a class of rough Fourier integral operators. Front. Math. China, 2023, 18(4): 235-249.
 链接本文:  
https://academic.hep.com.cn/fmc/CN/10.3868/s140-DDD-023-0019-x
https://academic.hep.com.cn/fmc/CN/Y2023/V18/I4/235
1 K Asada, D Fujiwara. On some oscillatory integral transformations in L2(Rn). Japan J Math (N S) 1978; 4(2): 299–361
2 R Beals. Spatially inhomogeneous pseudodifferential operators, II. Comm Pure Appl Math 1974; 27: 161–205
3 R Beals. Lp boundedness of Fourier integral operators. Mem Amer Math Soc 1982; 38(264): viii+57 pp
4 A P Calderón, R Vaillancourt. On the boundedness of pseudo-differential operators. J Math Soc Japan 1971; 23(2): 374–378
5 D Dos Santos Ferreira, W Staubach. Global and local regularity of Fourier integral operators on weighted and unweighted spaces. Mem Amer Math Soc 2014; 229(1074): xiv+65 pp
6 J Duistermaat, L Hörmander. Fourier integral operators, II. Acta Math 1972; 128(3/4): 183–269
7 G I Eskin. Degenerate elliptic pseudodifferential equations of principal type. Mat Sb (N S) 1970; 82(124): 585–628
8 A Greenleaf, G Uhlmann. Estimates for singular Radon transforms and pseudodifferential operators with singular symbols. J Funct Anal 1990; 89(1): 202–232
9 Y Higuchi, M Nagase. On the L2-boundedness of pseudo-differential operators. J Math Kyoto Univ 1988; 28(1): 133–139
10 L Hörmander. On the L2 continuity of pseudo-differential operators. Comm Pure Appl Math 1971; 24: 529–535
11 L Hörmander. Fourier integral operators, I. Acta Math 1971; 127(1/2): 79–183
12 C E Kenig, W Staubach. ψ-pseudodifferential operators and estimates for maximal oscillatory integrals. Studia Math 2007; 183(3): 249–258
13 M Peloso, S Secco. Boundedness of Fourier integral operators on Hardy spaces. Proc Edinburgh Math Soc 2008; 51(2): 443–463
14 J Peral. Lp estimates for the wave equation. J Funct Anal 1980; 36(1): 114–145
15 M Ruzhansky, M Sugimoto. Global L2-boundedness theorems for a class of Fourier integral operators. Comm Partial Differential Equations 2006; 31(4): 547–569
16 M Ruzhansky, M Sugimoto. A local-to-global boundedness argument and Fourier integral operators. J Math Anal Appl 2019; 473(2): 892–904
17 L Rodino. On the boundedness of pseudo differential operators in the class Lp,1m. Proc Amer Math Soc 1976; 58: 211–215
18 A Seeger, C D Sogge, E M Stein. Regularity properties of Fourier integral operators. Ann Math 1991; 134(2): 231–251
19 M SteinT S Murphy. Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. Princeton Mathematical Series, 43. Monographs in Harmonic Analysis, III. New Jersey: Princeton University Press, 1993
20 T Tao. The weak-type (1, 1) of Fourier integral operators of order −(n−1)/2. J Aust Math Soc 2004; 76(1): 1–21
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed