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Weak type estimates for Calderón-Zygmund operators on Herz spaces at critical indexes

✍ Scribed by Yasuo Komori

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 135 KB
Volume: 259
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310093

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✦ Synopsis

Abstract

We define weak Herz spaces $ \dot K ^{\alpha , p, \infty} _{q} $(ℝ^n^) which are the weak version of the ordinary Herz spaces $ \dot K ^{\alpha , p} _{q} $(ℝ^n^). We consider the boundedness of Calderón‐Zygmund operators from $ \dot K ^{\alpha , p} _{q} $ to $ \dot K ^{\alpha , p, \infty} _{q} $ at critical indexes α = −n/q, n(1− 1/q) and q = 1. We also consider weighted estimates. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Weak type estimates for some maximal ope

Weak type estimates for some maximal operators on Hardy spaces

✍ Ya Ryong Heo 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 144 KB

## Abstract We show that the lacunary maximal operator associated to a compact smooth hypersurface on which the Gaussian curvature nowhere vanishes to infinite order maps the standard Hardy space __H__ ^1^ to __L__ ^1,__∞__^ . (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)