Unimodular Fourier multipliers on homogeneous Besov spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:425

Article

Zhao, Guoping¹  Chen, Jiecheng²  Fan, Dashan³  Guo, Weichao⁴ 

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China

[3] Univ Wisconsin, Dept Math, Milwaukee, WI 53201 USA

[4] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

关键词: Fourier multipliers;    Homogeneous Besov space;    Sharpness;   

DOI  :  10.1016/j.jmaa.2014.12.035

来源: Elsevier

【 摘 要 】

In this paper, we study the Fourier multiplier operator e(i mu(D)) on homogeneous Besov spaces (B) over dot(p,q)(s). If mu is a homogeneous function with positive degree whose Hessian matrix is non-degenerate at some point, we find the necessary conditions of p(i) q(i), s(i) (i = 1,2) for the boundedness of e(i mu(D)) from (B) over dot(p1,q1)(s1) to (B) over dot(p2,q2)(s2). Moreover, under a global non-degenerate assumptions on the Hessian matrix of mu(xi), we obtain the sufficient and necessary conditions for the boundedness of e(i mu(D)) between (B) over dot(p1,q1)(s1) and (B) over dot(p2,q2)(s2). More precisely, we obtain the estimates of the operator norm parallel to e(i mu(D))parallel to((B) over dotp1,q1s1 -> (B) over dotp2,q2s2), and get the blowup rate near singularity points. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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