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- W3026320407 abstract "Recently, in cite{GXHTM}, the authors established $L^p$-boundedness of vector-valued $q$-variational inequalities for averaging operators which take values in the Banach space satisfying martingale cotype $q$ property. In this paper, we prove that martingale cotype $q$ property is also necessary for the vector-valued $q$-variational inequalities, which is a question left open. Moreover, we characterize UMD property and martingale cotype $q$ property in terms of vector valued $q$-variational inequalities for Hilbert transform." @default.
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- W3026320407 date "2020-05-22" @default.
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- W3026320407 title "Vector-valued q-variational inequalities for averaging operators and the Hilbert transform" @default.
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- W3026320407 doi "https://doi.org/10.1007/s00013-020-01472-1" @default.
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