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

Authors : Rüya Üster

Pages : 153-164

Doi:10.31801/cfsuasmas.1282587

View : 56 | Download : 120

Publication Date : 2024-03-16

Article Type : Research Paper

Abstract :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 $M(\\mathbb{A})$.
Keywords : Affine group, affine mapping, multiplier, weighted Orlicz space