Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


$ L\sp 2$ boundedness of highly oscillatory integrals on product domains

Author: Elena Prestini
Journal: Proc. Amer. Math. Soc. 104 (1988), 493-497
MSC: Primary 47G05; Secondary 42B20, 42B25
MathSciNet review: 962818
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove $ {L^2}$ boundedness of the oscillatory singular integral

$\displaystyle Tf(x,y) = \iint\limits_{{D_y}} {\frac{{\operatorname{exp} (2\pi iN(y)x')}}{{x'y'}}}f(x - x',y - y')dx'dy'$

where $ N(y)$ is an arbitrary integer-valued $ {L^\infty }$ function and where nothing is assumed on the dependency upon $ y$ of the domain of integration $ {D_y}$. We also prove $ {L^2}$ boundedness of the corresponding maximal opertaor. Operators of this kind appear in a problem of a.e. convergence of double Fourier series.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47G05, 42B20, 42B25

Retrieve articles in all journals with MSC: 47G05, 42B20, 42B25

Additional Information

PII: S 0002-9939(1988)0962818-0
Article copyright: © Copyright 1988 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia