The variable exponent Lebesgue function spaces close to L^\infty

Author: Shalva Zviadadze
Co-authors: Tengiz Kopaliani
Keywords: Variable exponent Lebesgue space, Decreasing rearrangement
Annotation:

In this talk we characterize those exponents $p(\cdot)$ for which corresponding variable exponent Lebesgue space $L^{p(\cdot)}([0;1])$ has in common with $L^\infty$ the property that the space of continuous functions is a closed linear subspace in it. In particular, we obtain necessary and sufficient condition on decreasing rearrangement of exponent $p(\cdot)$ for which exists equimeasurable exponent of $p(\cdot)$ which corresponding variable exponent Lebesgue space have the above mentioned property