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On symmetric spaces containing isomorphic copies of Orlicz sequence spaces

Astashkin S.

Commentationes Mathematicae

2016

Vol 56, No. 1

29--44

Let an Orlicz function N be (1+ε)-convex and (2−ε)-concave at zero for some ε>0. Then the function 1/N⁻¹(t), t∈(0,1], belongs to a separable symmetric space X with the Fatou property, which is an interpolation space with respect to the couple (L₁,L₂), whenever X contains a strongly embedded subspace isomorphic to the Orlicz sequence space l_N. On the other hand, we find necessary and sufficient conditions on such an Orlicz function N under which a sequence of mean zero independent functions equimeasurable with the function 1/N⁻¹(t), 0-1(t), a strongly embedded subspace isomorphic to the Orlicz sequence l_N.