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On the Operator L(f)=f log |f|

✍ Scribed by Tadeusz Iwaniec; Anne Verde

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 214 KB
Volume: 169
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1999.3443

No coin nor oath required. For personal study only.

✦ Synopsis

The present note deals with the operator L :

takes a given element f of the Hardy space to the function f log | f |. In general, this function need not be locally integrable. Nevertheless, due to peculiar cancellations of large positive and negative terms in the integral .f log | f | with . # C 0 (R n ), we are able to give meaning to f log | f | as a Schwartz distribution. We find several alternatives for this interpretation of f log | f |.

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On the Operator L(f)=f&#xa0;log&#xa0;|f|

✦ Synopsis

On the Operator L(f)=f log |f|