Full paper in PDF:
$%D. E. Edmunds and M. Krbec, Decomposition and Moser’s Lemma, Rev. Mat. Complut. 15
(2002), no. 1, 57–74.%$
Centre for Mathematical Analysis and Its Applications University of Sussex Falmer BN1 9QH — Great Britain | Institute of Mathematics Acad. Sci. of the Czech Republic Žitná 25, 115 67 Prague 1 — Czech Republic |
ABSTRACT
Using the idea of the optimal decomposition developed in recent papers (2000) by the same authors and in Cruz-Uribe et al. (to appear), we study the boundedness of the operator , , 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 (1971).
2000 Mathematics Subject Classification: 46E30, 26A12, 35A15, 35B10.