AbstractThe present note deals with the operator L:H1(Rn)→D′(Rn) which takes a given element f of the Hardy space to the function flog|f|. In general, this function need not be locally integrable. Nevertheless, due to peculiar cancellations of large positive and negative terms in the integral ∫ϕflog|f| with ϕ∈C∞0(Rn), we are able to give meaning to flog|f| as a Schwartz distribution. We find several alternatives for this interpretation of flog|f|
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