Global wave-front sets of Banach, Frechet and modulation space types, and pseudo-differential operators

被引：21

作者：

Coriasco, Sandro ^{[1
]}

Johansson, Karoline ^{[2
]}

Toft, Joachim ^{[2
]}

机构：

[1] Univ Turin, Dipartimento Matemat, I-10124 Turin, Italy

[2] Linnaeus Univ, Dept Comp Sci Phys & Math, Vaxjo, Sweden

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年 / 254卷 / 08期

关键词：

Wave front; Fourier; Banach space; Modulation space; Micro-local; Pseudo-differential;

D O I：

10.1016/j.jde.2013.01.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce global wave-front sets WFB(f), f is an element of'(R-d), with respect to suitable Banach or Frechet spaces B. An important special case is given by the modulation spaces B = M(omega,B), where omega is an appropriate weight function and B is a translation invariant Banach function space. We show that the standard properties for known notions of wave-front set extend to WFB(f). In particular, we prove that micro-locality and micro-ellipticity hold for a class of globally defined pseudo-differential operators Op(t)(alpha), acting continuously on the involved spaces. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：3228 / 3258

页数：31

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