Extends asymptotic results for lacunary series to nonlinear functionals f_k and proves Kadec-Pelczynski type theorems in Orlicz spaces.
A Marcinkiewicz-Zygmund inequality and the Kadec Pe{\l}czyn\'ski theorem in Orlicz spaces
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abstract
In this paper, we extend the Marcinkiewicz--Zygmund inequality to the setting of Orlicz and Lorentz spaces. Furthermore, we generalize a Kadec--Pe{\l}czy\'nski-type result -- originally established by the first and third authors for $L^p$ spaces with $1 \le p < 2$ -- to a broader class of Orlicz spaces defined via Young functions $\psi$ satisfying $x \le \psi(x) \le x^2$.
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math.FA 1years
2026 1verdicts
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Lacunary Series, Nonlinear Functionals and Banach Space Structure
Extends asymptotic results for lacunary series to nonlinear functionals f_k and proves Kadec-Pelczynski type theorems in Orlicz spaces.