Abstract
We study Fubini-type property for Lorentz spaces Lp,r (ℝ2). This problem is twofold. First we assume that all linear sections of a function f in directions of coordinate axes belong to Lp,r(ℝ), and their one-dimensional Lp,r-norms belong to Lp,r(ℝ). We show that for p ≠ r it does not imply that f ∇ Lp,r(ℝ2) (this complements one result by Cwikel). Conversely, we assume that f ∇ Lp,r(ℝ2), and we show that then for r < p almost all linear sections of f belong to Lp,r(ℝ), but for p < r all linear sections may have infinite one-dimensional Lp,r-norms. © Springer Science+Business Media, LLC 2013.
Cite
CITATION STYLE
Kolyada, V. I. (2013). On Fubini Type Property in Lorentz Spaces. In Springer Proceedings in Mathematics and Statistics (Vol. 25, pp. 171–179). Springer New York LLC. https://doi.org/10.1007/978-1-4614-4565-4_16
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