What question did this study set out to answer?

The aim is to explore the structure of subsymmetric basic sequences in variable exponent Lebesgue spaces L^P.

May 24, 2026Open Access

On the Basic Sequence Structure of Variable Exponent Lebesgue Spaces

Key Points

The aim is to explore the structure of subsymmetric basic sequences in variable exponent Lebesgue spaces L^P.
Analyzed basic sequence structures in variable exponent Lebesgue spaces using index functions P.
Proved the equivalence of complemented subsymmetric basic sequences to canonical bases for specific indices.
Investigated the relationship between essential ranges of the variable exponent P and their implications for basic sequences.
Established that if P is bounded away from infinity, any complemented subsymmetric basic sequence of L^P is equivalent to the canonical basis of r for some r in the essential range of P.

Abstract

We study the subsymmetric basic sequence structure of variable exponent Lebesgue spaces L P built from index functions P : (0, ] on -finite m easure s paces (, , ).Specifically, we prove that if P is bounded away from infinity, t hen a ny complemented subsymmetric basic sequence of L P is equivalent to the canonical basis of r for some r 1 in the essential range of P .The paper that initiated the study of variable exponent Lebesgue spaces by basic sequence techniques was 11 (see also 10).In it, the authors characterized in terms of the essential range of the variable exponent P the indices q [1, ) such that q isomorphically embeds

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