Affine mappings and multipliers for weighted Orlicz spaces over the affine group $mathbb{R}_{+}times mathbb{R}$

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Üster R.

Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, cilt.73, sa.1, ss.153-164, 2024 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 73 Sayı: 1
• Basım Tarihi: 2024
• Doi Numarası: 10.31801/cfsuasmas.1282587
• Dergi Adı: Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.153-164
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• İstanbul Üniversitesi Adresli: Evet

Özet

Let $mathbb{A}=mathbb{R}_{+}times mathbb{R}$ be the affine group with a right Haar measure $mu$, $omega$ be a weight function on $mathbb{A}$ and $Phi$ be a Young function. We characterize the affine continuous mappings on the subsets of $L^Phi(mathbb{A},omega)$. Moreover we show that there exists an isometric isomorphism between the multiplier for the pair $(L^{1}(mathbb{A})cap L^{Phi}(mathbb{A}),L^{1}(mathbb{A}))$ and the space of bounded measures $M(mathbb{A})$.