A convolution property of the Cantor-Lebesgue measure, II

Daniel M. Oberlin

Colloquium Mathematicae, Tome 96 (2003), p. 23-28 / Harvested from The Polish Digital Mathematics Library

Résumé

For 1 ≤ p,q ≤ ∞, we prove that the convolution operator generated by the Cantor-Lebesgue measure on the circle is a contraction whenever it is bounded from $L^{p} ()$ to $L^{q} ()$ . We also give a condition on p which is necessary if this operator maps $L^{p} ()$ into L²().

Publié le : 2003-01-01

Zbl 1095.42007

EUDML-ID : urn:eudml:doc:284489

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     author = {Daniel M. Oberlin},
     title = {A convolution property of the Cantor-Lebesgue measure, II},
     journal = {Colloquium Mathematicae},
     volume = {96},
     year = {2003},
     pages = {23-28},
     zbl = {1095.42007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-1-3}
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Daniel M. Oberlin. A convolution property of the Cantor-Lebesgue measure, II. Colloquium Mathematicae, Tome 96 (2003) pp. 23-28. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-1-3/