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Opposed Exponent Profiles and Real Interpolation of Measurable Subspaces
We study real interpolation of the $G$-measurable subspaces $Y_j$ of variable Lebesgue spaces $L^{p_j(\cdot)}$. For a family of continuous exponent pairs that vary in opposite directions on the atoms of $G$, we prove that $K$-closedness is equivalent to a uniform logarithmic bound on the oscillation
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