Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the norms of discrete analogues of convolution operators


Author: Oleg Kovrizhkin
Journal: Proc. Amer. Math. Soc. 140 (2012), 1349-1352
MSC (2010): Primary 42A99, 42B99
Published electronically: August 4, 2011
MathSciNet review: 2869118
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider a discrete analogue of convolution operator $ T(f) = K*f$ from $ L^p({\mathbb{R}}^d)$ to $ L^p({\mathbb{R}}^d)$: $ T_{dis}(g) = K_{dis}* g$ from $ \ell^p(\mathbb{Z}^d)$ to $ \ell^p(\mathbb{Z}^d)$ where $ K_{dis} = K \vert_{\mathbb{Z}^d}$ and $ \hat K$ is supported in the fundamental cube. We show that the estimate $ \Vert T_{dis}\Vert _p \le C^d \Vert T\Vert _p$ with $ C > 1$ cannot be improved for a certain range of $ p$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 42A99, 42B99

Retrieve articles in all journals with MSC (2010): 42A99, 42B99


Additional Information

Oleg Kovrizhkin
Email: olegk@alum.mit.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11043-8
PII: S 0002-9939(2011)11043-8
Keywords: Discrete analogues, convolutions.
Received by editor(s): December 16, 2010
Received by editor(s) in revised form: January 4, 2011
Published electronically: August 4, 2011
Additional Notes: This research was partially supported by NSF grant DMS 0201099
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2011 American Mathematical Society