Special John-Nirenberg-Campanato spaces via congruent cubes
type: Item
instance of: scholarly article
title: Special John-Nirenberg-Campanato spaces via congruent cubes
zbMATH Open document ID: 1489.42013
author: Hongchao Jia
author: Jin Tao
author: Wen Yuan
author: Yangyang Zhang
author: Dachun Yang
published in: Science China. Mathematics
publication date: 2022-03-04T00:00:00Z
review text: Let \(p\in [1,\infty)\), \(q \in [1,\infty)\), \(\alpha \in {\mathbb R}\), and \(s\) be a non-negative integer. Inspired by the space \(JN_p\) introduced by \textit{F. John} and \textit{L. Nirenberg} [Commun. Pure Appl. Math. 14, 415--426 (1961; Zbl 0102.04302)] and the space \(B\) introduced by \textit{J. Bourgain} et al. [J. Eur. Math. Soc. (JEMS) 17, No. 9, 2083--2101 (2015; Zbl 1339.46028)], we introduce a special John-Nirenberg-Campanato space \(JN^{\mathrm{con}}_ {(p,q,s)_{\alpha}}\) over \({\mathbb R}^n\) or a given cube of \({\mathbb R}^n\) with finite side length via congruent subcubes, which are of some amalgam features. The limit space of such spaces as \(p\to \infty\) is just the Campanato space which coincides with the space BMO (the space of functions with bounded mean oscillations) when \(\alpha = 0\). Moreover, a vanishing subspace of this new space is introduced, and its equivalent characterization is established as well, which is a counterpart of the known characterization for the classical space VMO (the space of functions with vanishing mean oscillations) over \({\mathbb R}^n\) or a given cube of \({\mathbb R}^n\) with finite side length. Furthermore, some VMO-\(H_{1}\)-BMO-type results for this new space are also obtained, which are based on the aforementioned vanishing subspaces and the Hardy-type space defined via congruent cubes in this article. The geometrical properties of both the Euclidean space via its dyadic system and congruent cubes play a key role in the proof of all these results.
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 7484068
zbMATH Keywords: John-Nirenberg space
zbMATH Keywords: congruent cube
zbMATH Keywords: amalgam Campanato space
zbMATH Keywords: Hardy-type space
zbMATH Keywords: duality
zbMATH Keywords: vanishing subspace
zbMATH Keywords: BMO
Wikidata QID: Q114222411
MaRDI profile type: Publication
full work available at URL: s11425-021-1866-4
OpenAlex ID: W4206549188
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DOI: 10.1007/S11425-021-1866-4
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