Multipliers on generalized mixed norm sequence spaces
type: Item
instance of: scholarly article
title: Multipliers on generalized mixed norm sequence spaces
zbMATH Open document ID: 1474.42028
DOI: 10.1155/2014/983273
author: Oscar Blasco
author: Carme Zaragoza-Berzosa
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Given \(1 \leq p\), \(q \leq \infty\) and sequences of integers \((n_k)_k\) and \((n_k')_k\) such that \(n_k \leq n_k' \leq n_{k + 1}\), the generalized mixed norm space \(\ell^{\mathcal{I}}(p, q)\) is defined as those sequences \((a_j)_j\) such that \(((\sum_{j \in I_k} |a_j|^p)^{1 / p})_k \in \ell^q\) where \(I_k = \{j \in \mathbb N_0 \text{s.t.} n_k \leq j < n_k' \}\), \(k \in \mathbb N_0\). The necessary and sufficient conditions for a sequence \(\lambda = (\lambda_j)_j\) to belong to the space of multipliers \((\ell^{\mathcal{I}}(r, s), \ell^{\mathcal{J}}(u, v))\), for different sequences \(\mathcal{I}\) and \(\mathcal{J}\) of intervals in \(\mathbb N_0\), are determined.
Mathematics Subject Classification ID: 42A45
Mathematics Subject Classification ID: 40A05
zbMATH DE Number: 7023453
Wikidata QID: Q59043300
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/983273
OpenAlex ID: W2023916918
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description: scientific article; zbMATH DE number 7023453