Littlewood-Paley characterizations of Triebel-Lizorkin-Morrey spaces via ball averages

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• 作者：Junwei Zhang^a ; ^{junbao@mail.bnu.edu.cn} ; Ciqiang Zhuo^b ; ^{cqzhuo@mail.bnu.edu.cn} ; Dachun Yang^a ; ^{dcyang@bnu.edu.cn} ; Ziyi He^a ; ^{ziyihe@mail.bnu.edu.cn}
• 关键词：primary ; 46E35 ; secondary ; 42B25 ; 42B35
• 刊名：Nonlinear Analysis: Theory, Methods & Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：150
• 期：Complete
• 页码：76-103
• 全文大小：825 K
• 卷排序：150

文摘

Let 1<p≤u<∞1<p≤u<∞ and q∈(1,∞]q∈(1,∞]. In this article, the authors establish equivalent characterizations of the Triebel–Lizorkin–Morrey space Eu,q,pα(Rn) with smoothness order α∈(0,2)α∈(0,2) in terms of the Lusin-area function and the gλ∗-function generated by the difference between f(x)f(x) and its ball average B2−jf(x):=1|B(x,2−j)|∫B(x,2−j)f(y)dy,&forall;j∈{1,2,…},&forall;x∈Rn, where, for any j∈{1,2,…}j∈{1,2,…} and x∈Rnx∈Rn, B(x,2−j):={y∈Rn:|y−x|<2−j}. As applications, the authors obtain several characterizations of Eu,∞,pα(Rn) via pointwise inequalities involving ball averages.