Disjointly strictly singular inclusions between variable Lebesgue spaces
arxiv(2024)
摘要
Disjointly strictly singular inclusions between variable Lebesgue spaces
L^p(·)(μ) on finite measure are characterized. Suitable criteria in
terms of the (bounded or unbounded) exponents are given. It is proved the
equivalence of L-weak compactness (also called almost compactness) and
disjoint strict singularity for variable Lebesgue space inclusions. For
infinite measure any inclusion L^p(·)(μ) ↪
L^q(·)(μ) is not disjointly strictly singular. No restrictions on the
exponent are imposed.
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