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- W2891284257 abstract "Necessary and sufficient conditions for the weight function $u$ are obtained, which provide the boundedness for a class of averaging operators from $L_p^+$ to $L_{q,u}^+$. These operators include the multiple Hardy-Littlewood averages and related maximal operators, geometric mean operators, and geometric maximal operators. We show that, under suitable conditions, the boundedness of these operators are equivalent. Our theorems extend several one-dimensional results to multi-dimensional cases and to operators with multiple kernels. We also show that in the case $p<q$, some one-dimensional results do not carry over to the multi-dimensional cases, and the boundedness of $T$ from $L_p^+$ to $L_{q,u}^+$ holds only if $u=0$ almost everywhere." @default.
- W2891284257 created "2018-09-27" @default.
- W2891284257 creator A5012122532 @default.
- W2891284257 date "2018-09-05" @default.
- W2891284257 modified "2023-09-27" @default.
- W2891284257 title "On the equivalence of boundedness for multiple Hardy-Littlewood averages and related operators" @default.
- W2891284257 doi "https://doi.org/10.7146/math.scand.a-105662" @default.
- W2891284257 hasPublicationYear "2018" @default.
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