Using the idea of the optimal decomposition developed in recent papers (Edmunds-Krbec, 2000) and in Cruz-Uribe-Krbec we study the boundedness of the operator Tg(x) = ∫x 1 g(u)du / u, x ∈ (0,1), and its logarithmic variant between Lorentz spaces and exponential Orlicz and Lorentz-Orlicz spaces. These operators are naturally linked with Moser's lemma, O'Neil's convolution inequality, and estimates for functions with prescribed rearrangement. We give sufficient conditions for and very simple proofs of uniform boundedness of exponential and double exponential integrals in the spirit of the celebrated lemma due to Moser.
@article{urn:eudml:doc:44425,
title = {Decomposition and Moser's lemma.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {15},
year = {2002},
pages = {57-74},
zbl = {1017.46020},
mrnumber = {MR1915215},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44425}
}
Edmunds, David E.; Krbec, Miroslav. Decomposition and Moser's lemma.. Revista Matemática de la Universidad Complutense de Madrid, Tome 15 (2002) pp. 57-74. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44425/