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Journals / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 2

On Lipschitz-Lorentz spaces and their Zygmund classes

İlker ERYILMAZ
Cenap DUYAR
Pages
159–169
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, we characterize the space of multipliers from Lorentz spaces to the Lipschitz-Lorentz-Zygmund classes L$Lambda_*$($alpha$ , pq;G) and L$lambda_*$( $alpha$, pq;G).

📌 3 Key Takeaways

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Objective & Hypothesis:Let G be a metrizable locally compact abelian group.
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Key Findings & Data:We prove that ($L _1$(G), lip($alpha,pq$), $widetilde {lip(alpha,pq)}$, ($L _1$(G), Lip ( $alpha$, pq)) and Lip ($alpha$ , pq) are isometrically isomorphic, where Lip ( $alpha$$, pq) and lip ($alpha$ , pq) denote the Lipschitz-Lorentz spaces defined on G, ($L _1$(G),A) is the space of multipliers from $L _1$(G) to A and $widetilde {lip(alpha,pq)}$ denotes the relative completion of lip ( $alpha$, pq).
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Conclusion & Impact:Also, we characterize the space of multipliers from Lorentz spaces to the Lipschitz-Lorentz-Zygmund classes L$Lambda_*$($alpha$ , pq;G) and L$lambda_*$( $alpha$, pq;G).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Let G be a metrizable locally compact abelian group. We prove that ($L _1$(G), lip($alpha,pq$), $widetilde {lip(alpha,pq)}$, ($L _1$(G), Lip ( $alpha$, pq)) and Lip ($alpha$ , pq) are isometrically isomorphic, where Lip ( $alpha$$, pq) and lip ($alpha$ , pq) denote the Lipschitz-Lorentz spaces defined on G, ($L _1$(G),A) is the space of multipliers from $L _1$(G) to A and $widetilde {lip(alpha,pq)}$ denotes the relative completion of lip ( $alpha$, pq). Also, we characterize the space of multipliers from Lorentz spaces to the Lipschitz-Lorentz-Zygmund classes L$Lambda_*$($alpha$ , pq;G) and L$lambda_*$( $alpha$, pq;G).

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Cite This Article

ERYILMAZ, İ., DUYAR, C. (2022). On Lipschitz-Lorentz spaces and their Zygmund classes. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 2, 159–169. https://ajindex.com/articles/530615

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