Geodesic
Translation-invariant operators on Lorentz spaces $L(1,q)$ with $0 q 1$
Studia Mathematica, Tome 132 (1999) no. 2, pp. 101-124

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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.
DOI : 10.4064/sm-132-2-101-124
Keywords: Lorentz space, convolution operator

Leonardo Colzani, Peter Sjögren 1

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Leonardo Colzani, Peter Sjögren. Translation-invariant operators on Lorentz spaces $L(1,q)$ with $0 < q < 1$. Studia Mathematica, Tome 132 (1999) no. 2, pp. 101-124. doi: 10.4064/sm-132-2-101-124

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