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The Quarterly Journal of Mathematics 2004 55(1):41-45; doi:10.1093/qmath/hag032
© 2004 by Oxford University Press
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A useful estimate for the decreasing rearrangement of the sum of functions

María J. Carro1 and Joaquim Martín1

1 Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, E-08071 Barcelona, Spain

Given f={sum}nN fn, where {fn}n are measurable functions, we show that f*(3t)≤{sum}n ( fn*(t) +1/t {int}cnttfn*(s) ds ), where {cn}nN are positive numbers such that {sum}n cn=1. Several consequences in the setting of weighted Lorentz spaces are also given.

Received 12 October 2001.


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