L2-estimates for singular oscillatory integral operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:441

Article

Aleksanyan, Hayk^1,2  Shahgholian, Henrik²  Sjolin, Per² 

[1] Univ Edinburgh, Sch Math, JCMB Kings Bldg,Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Midlothian, Scotland

[2] KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

关键词: Singular integral;    Oscillating surface;    Maximal operator;    Helmholtz equation;   

DOI  :  10.1016/j.jmaa.2016.04.031

来源: Elsevier

【 摘 要 】

In this note we study singular oscillatory integrals with linear phase function over hypersurfaces which may oscillate, and prove estimates of L-2 bar right arrow L-2 type for the operator, as well as for the corresponding maximal function. If the hypersurface is flat, we consider a particular class of a nonlinear phase functions, and apply our analysis to the eigenvalue problem associated with the Helmholtz equation in R-3. (c) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free