Geodesic
On the Normability of Marcinkiewicz Classes
Matematičeskie zametki, Tome 81 (2007) no. 4, pp. 483-489

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We obtain simple necessary and sufficient conditions for the normability of Marcinkiewicz classes, which play an important role in various problems of analysis. These conditions are stated in terms of dilation exponents of the function generating the given class as well as in terms of interpolation for operators bounded in the couple $(L_1,L_\infty)$.
Mots-clés : Marcinkiewicz class, interpolation, quasinorm
Keywords: normability, generating function, dilation exponent, Hardy–Littlewood operator, symmetric Banach space. 
@article{MZM_2007_81_4_a0,
     author = {S. V. Astashkin},
     title = {On the {Normability} of {Marcinkiewicz} {Classes}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--489},
     publisher = {mathdoc},
     volume = {81},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a0/}
}
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S. V. Astashkin. On the Normability of Marcinkiewicz Classes. Matematičeskie zametki, Tome 81 (2007) no. 4, pp. 483-489. http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a0/