Duality in spaces of finite linear combinations of atoms

Fulvio Ricci, Joan Verdera

Research output: Contribution to journalArticleResearchpeer-review

12 Citations (Scopus)

Abstract

In this paper we describe the dual and the completion of the space of finite linear combinations of (p,∞)-atoms, 0 < p ≤ 1. As an application, we show an extension result for operators uniformly bounded on (p,∞)-atoms, 0 < p < 1, whose analogue for p = 1 is known to be false. Let 0 < p < 1 and let T be a linear operator defined on the space of finite linear combinations of (p,∞)-atoms, 0 < p < 1, which takes values in a Banach space B. If T is uniformly bounded on (p,∞)-atoms, then T extends to a bounded operator from Hp(ℝn) into B.© 2010 American Mathematical Society.
Original languageEnglish
Pages (from-to)1311-1323
JournalTransactions of the American Mathematical Society
Volume363
Issue number3
DOIs
Publication statusPublished - 1 Mar 2011

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