Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1

Colzani, Leonardo; Sjögren, Peter

Studia Mathematica, Tome 133 (1999), p. 101-124 / Harvested from The Polish Digital Mathematics Library

Résumé

We study convolution operators bounded on the non-normable Lorentz spaces $L^{1, q}$ of the real line and the torus. Here 0 < q < 1. On the real line, such an operator is given by convolution with a discrete measure, but on the torus a convolutor can also be an integrable function. We then give some necessary and some sufficient conditions for a measure or a function to be a convolutor on $L^{1, q}$ . In particular, when the positions of the atoms of a discrete measure are linearly independent over the rationals, we give a necessary and sufficient condition. This condition is, however, only sufficient in the general case.

Publié le : 1999-01-01

Zbl 0921.42004

EUDML-ID : urn:eudml:doc:216589

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     title = {Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1},
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     volume = {133},
     year = {1999},
     pages = {101-124},
     zbl = {0921.42004},
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Colzani, Leonardo; Sjögren, Peter. Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1. Studia Mathematica, Tome 133 (1999) pp. 101-124. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv132i2p101bwm/

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