TY  - JOUR
T1  - A criterion for nonzero multiplier for Orlicz spaces of an affine group $\mathbb{R}_{+}\times \mathbb{R}$
AU  - Üster, Rüya
PY  - 2023
DA  - October
DO  - 10.15672/hujms.1175682
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1198
EP  - 1205
VL  - 52
IS  - 5
LA  - en
AB  - 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.
KW  - Affine group
KW  - Orlicz space
KW  - nonzero multiplier
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UR  - https://doi.org/10.15672/hujms.1175682
L1  - https://dergipark.org.tr/en/download/article-file/2652279
ER  -