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- W2742279024 abstract "Let $Phi_1$ and $Phi_2$ be nondecreasing functions from $mathbb{R_+}=(0,infty)$ onto itself. For $i=1,2$ and $gamma in mathbb{R}$, define the Orlicz class $L_{Phi_{i}}(mathbb{R_+})$ to be the set of Lebesgue-measurable functions $f$ on $mathbb{R_+}$ such that begin{equation*} int_{mathbb{R_+}} Phi_{i} left( k|(Tf)(t)| right) t^{gamma}dt 0$. Our goal in this paper is to find conditions on $Phi_1$, $Phi_2$, $gamma$ and an operator $T$ so that the assertions begin{equation} T : L_{Phi_2,t^{gamma}}(mathbb{R_+}) rightarrow L_{Phi_1,t^{gamma}}(mathbb{R_+}), tag{I} end{equation} and begin{equation}label{modularA} int_{mathbb{R_+}} Phi_1 left( |(Tf)(t)| right)t^{gamma}dt leq K int_{mathbb{R_+}} Phi_2 left( K|f(s)| right)s^{gamma}ds, tag{M} end{equation} in which $K>0$ is independent of $f$, say, simple on $mathbb{R_+}$, are equivalent and to then find necessary and sufficient conditions in order that (ref{modularA}) holds." @default.
- W2742279024 created "2017-08-17" @default.
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- W2742279024 date "2017-08-04" @default.
- W2742279024 modified "2023-09-27" @default.
- W2742279024 title "Dilation-commuting operators on power-weighted Orlicz classes" @default.
- W2742279024 hasPublicationYear "2017" @default.
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