Geodesic
On a theorem of Marcinkiewicz type for $H$-valued functions. A~continual form of the Paley--Littlewood theorem
Sbornik. Mathematics, Tome 16 (1972) no. 2, pp. 237-243

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In this report there are proved theorems on the boundedness of the convolution operator acting from the space $L_p(H')$ ($p$-summable functions on the line with values in the Hilbert space $(H')$ into the space $L_p(H'')$. There is derived a new version of the Paley–Littlewood Theorem. Bibliography: 3 items. 
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     author = {P. I. Lizorkin},
     title = {On a theorem of {Marcinkiewicz} type for $H$-valued functions. {A~continual} form of the {Paley--Littlewood} theorem},
     journal = {Sbornik. Mathematics},
     pages = {237--243},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_16_2_a6/}
}
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P. I. Lizorkin. On a theorem of Marcinkiewicz type for $H$-valued functions. A~continual form of the Paley--Littlewood theorem. Sbornik. Mathematics, Tome 16 (1972) no. 2, pp. 237-243. http://geodesic.mathdoc.fr/item/SM_1972_16_2_a6/