Lebesgue spaces with variable exponent on a probability space
Aoyama, Hiroyuki
Hiroshima Math. J., Tome 39 (2009) no. 1, p. 207-216 / Harvested from Project Euclid
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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.
Publié le : 2009-07-15
Classification:  Generalized Lebesgue space,  variable exponent,  martingale,  Doob's inequality,  46E30,  60G42 
@article{1249046337,
     author = {Aoyama, Hiroyuki},
     title = {Lebesgue spaces with variable exponent on a probability space},
     journal = {Hiroshima Math. J.},
     volume = {39},
     number = {1},
     year = {2009},
     pages = { 207-216},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1249046337}
}

Aoyama, Hiroyuki. Lebesgue spaces with variable exponent on a probability space. Hiroshima Math. J., Tome 39 (2009) no. 1, pp.  207-216. http://gdmltest.u-ga.fr/item/1249046337/