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

Remote Access
St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)



Littlewood-Paley inequality for arbitrary rectangles in $ \mathbb{R}^2$ for  $ 0 < p \le 2$

Author: N. N. Osipov
Translated by: The author
Original publication: Algebra i Analiz, tom 22 (2010), nomer 2.
Journal: St. Petersburg Math. J. 22 (2011), 293-306
MSC (2010): Primary 42B25, 42B15
Published electronically: February 8, 2011
MathSciNet review: 2668127
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The one-sided Littlewood-Paley inequality for pairwise disjoint rectangles in $ \mathbb{R}^2$ is proved for the $ L^p$-metric, $ 0 < p \le 2$. This result can be treated as an extension of Kislyakov and Parilov's result (they considered the one-dimensional situation) or as an extension of Journé's result (he considered disjoint parallelepipeds in $ \mathbb{R}^n$ but his approach is only suitable for $ p\in(1,2]$). We combine Kislyakov and Parilov's methods with methods ``dual'' to Journé's arguments.

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

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 42B25, 42B15

Retrieve articles in all journals with MSC (2010): 42B25, 42B15

Additional Information

N. N. Osipov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, 27 Fontanka, St. Petersburg 191023, Russia

Keywords: Littlewood–Paley inequality, Hardy class, atomic decomposition, Journé lemma, Calderón–Zygmund operator
Received by editor(s): September 11, 2009
Published electronically: February 8, 2011
Additional Notes: The author was supported by RFBR (grant no. 08-01-00358)
Article copyright: © Copyright 2011 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