A criterion for nonzero multiplier for Orlicz spaces of an affine group R + × R

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Atıf İçin Kopyala

Üster R.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.52, sa.5, ss.1198-1205, 2023 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 52 Sayı: 5
• Basım Tarihi: 2023
• Doi Numarası: 10.15672/hujms.1175682
• Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
• Sayfa Sayıları: ss.1198-1205
• İstanbul Üniversitesi Adresli: Evet

Özet

Let A=R+×R" role="presentation" >A=R+×R$\mathbb{�}={\mathbb{�}}_{+}\times \mathbb{�}$ be an affine group with right Haar measure dμ" role="presentation" >dμ$��$ and Φi" role="presentation" >Φi${\mathrm{\Phi }}_{�}$, i=1,2" role="presentation" >i=1,2$�=1,2$, be Young functions. We show that there exists an isometric isomorphism between the multiplier of the pair (LΦ1(A),LΦ2(A))" role="presentation" >(LΦ1(A),LΦ2(A))$({�}^{{\mathrm{\Phi }}_1}(\mathbb{�}),{�}^{{\mathrm{\Phi }}_2}(\mathbb{�}))$ and (LΨ2(A),LΨ1(A))" role="presentation" >(LΨ2(A),LΨ1(A))$({�}^{{\mathrm{\Psi }}_2}(\mathbb{�}),{�}^{{\mathrm{\Psi }}_1}(\mathbb{�}))$ where Ψi" role="presentation" >Ψi${\mathrm{\Psi }}_{�}$ are complementary pairs of Φi" role="presentation" >Φi${\mathrm{\Phi }}_{�}$, i=1,2" role="presentation" >i=1,2$�=1,2$, respectively. Moreover we show that under some conditions there is no nonzero multiplier for the pair (LΦ1(A),LΦ2(A))" role="presentation" >(LΦ1(A),LΦ2(A))$({�}^{{\mathrm{\Phi }}_1}(\mathbb{�}),{�}^{{\mathrm{\Phi }}_2}(\mathbb{�}))$, i.e., for an affine group A" role="presentation" >A$\mathbb{�}$ only the spaces M(LΦ1(A),LΦ2(A))" role="presentation" >M(LΦ1(A),LΦ2(A))$�({�}^{{\mathrm{\Phi }}_1}(\mathbb{�}),{�}^{{\mathrm{\Phi }}_2}(\mathbb{�}))$, with a concrete condition, are of any interest.