A criterion for nonzero multiplier for Orlicz spaces of an affine group $\\mathbb{R}_{+}\\times \\mathbb{R}$

Authors : Rüya Üster

Pages : 1198-1205

Doi:10.15672/hujms.1175682

View : 214 | Download : 189

Publication Date : 2023-10-31

Article Type : Research Paper

Abstract :Let $\\mathbb{A}=\\mathbb{R}_{+}\\times \\mathbb{R}$ be an affine group with right Haar measure $d\\mu$ and $\\Phi_i$, $i=1,2$, be Young functions. We show that there exists an isometric isomorphism between the multiplier of the pair $(L^{\\Phi_1}(\\mathbb{A}),L^{\\Phi_2}(\\mathbb{A}))$ and $(L^{\\Psi_2}(\\mathbb{A}),L^{\\Psi_1}(\\mathbb{A}))$ where $\\Psi_i$ are complementary pairs of $\\Phi_i$, $i=1,2$, respectively. Moreover we show that under some conditions there is no nonzero multiplier for the pair $(L^{\\Phi_1}(\\mathbb{A}),L^{\\Phi_2}(\\mathbb{A}))$, i.e., for an affine group $\\mathbb{A}$ only the spaces $M(L^{\\Phi_1}(\\mathbb{A}),L^{\\Phi_2}(\\mathbb{A}))$, with a concrete condition, are of any interest.
Keywords : Affine group, Orlicz space, nonzero multiplier