Abstract
We show that the Lebesgue space with a variable exponent $L_{p(\cdot )}$ is a rearrangement--invariant space if and only if $p$ is constant. In addition, we give a necessary and sufficient condition on a variable exponent for a martingale inequality to hold.
Citation
Hiroyuki Aoyama. "Lebesgue spaces with variable exponent on a probability space." Hiroshima Math. J. 39 (2) 207 - 216, July 2009. https://doi.org/10.32917/hmj/1249046337
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