Provides necessary conditions for strictly and finitely strictly singular embeddings in variable Lebesgue spaces, highlighting their dependence on exponents.
For two variable Lebesgue spaces and , with , we provide necessary and sufficient conditions under which the natural embeddings are strictly or finitely strictly singular. We also provide estimates for the Bernstein numbers of the natural embedding and show how they depend on the exponents and .
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Lang et al. (2025) studied this question.
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