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Journals / Düzce Üniversitesi Bilim ve Teknoloji Dergisi / 2021 / Cilt: 9 - Sayı: 4

Some New Results on the Banach Space A_{p1,q1}^{p2,q2}(G,w)

A_{p1,q1}^{p2,q2}(G,w) Banach Uzayı Üzerindeki Bazı Yeni Sonuçlar

Nilay DEĞİRMEN
Pages
1420–1435
Publication Date
2021-07-31
DOI
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⚡ TL;DR(Too Long; Didn't Read)

Also, if the weight w provides some special conditions, an approximate identity for the space A_{p1,q1}^{p2,q2}(G,w) has been obtained in the weighted Lorentz space Λ_G^1 (w) and it has been proved that the space A_{p1,q1}^{p2,q2}(G,w) is a Banach right Λ_G^1 (w)-module.

📌 3 Key Takeaways

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Objective & Hypothesis:Let G be a unimodular locally compact group and w∈Bp where p=min{p1,p2} .
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Key Findings & Data:In this work, in the case of changing indices, the inclusion properties of the space A_{p1,q1}^{p2,q2}(G,w) have been examined.
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Conclusion & Impact:Also, if the weight w provides some special conditions, an approximate identity for the space A_{p1,q1}^{p2,q2}(G,w) has been obtained in the weighted Lorentz space Λ_G^1 (w) and it has been proved that the space A_{p1,q1}^{p2,q2}(G,w) is a Banach right Λ_G^1 (w)-module.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:ağırlık · banach sağ A-modül · girişim operatörü

Abstract

Let G be a unimodular locally compact group and w∈Bp where p=min{p1,p2} . In this work, in the case of changing indices, the inclusion properties of the space A_{p1,q1}^{p2,q2}(G,w) have been examined. Also, if the weight w provides some special conditions, an approximate identity for the space A_{p1,q1}^{p2,q2}(G,w) has been obtained in the weighted Lorentz space Λ_G^1 (w) and it has been proved that the space A_{p1,q1}^{p2,q2}(G,w) is a Banach right Λ_G^1 (w)-module.

Özet

G ünimodüler yerel kompakt grup ve p=min{p1,p2} olmak üzere w∈Bp olsun. Bu çalışmada, A_{p1,q1}^{p2,q2}(G,w) uzayının indislerin değişmesi durumunda kapsama özellikleri incelenmiştir. Ayrıca w ağırlığının bazı özel şartları sağlaması durumunda A_{p1,q1}^{p2,q2}(G,w) uzayı için Λ_G^1 (w) ağırlıklı Lorentz uzayında bir yaklaşık birim elde edilmiş ve A_{p1,q1}^{p2,q2}(G,w) uzayının bir Banach sağ Λ_G^1 (w)-modül olduğu ispatlanmıştır.

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Cite This Article

DEĞİRMEN, N. (2021). Some New Results on the Banach Space A_{p1,q1}^{p2,q2}(G,w). Düzce Üniversitesi Bilim ve Teknoloji Dergisi, Cilt: 9 - Sayı: 4, 1420–1435. https://ajindex.com/articles/660895

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