On some subspaces of Morrey-Sobolev spaces and boundedness of Riesz integrals

Mouhamadou Dosso ; Ibrahim Fofana ; Moumine Sanogo

Annales Polonici Mathematici, Tome 107 (2013), p. 133-153 / Harvested from The Polish Digital Mathematics Library

Résumé

For 1 ≤ q ≤ α ≤ p ≤ ∞, $(L^q,l^p)^{α}$ is a complex Banach space which is continuously included in the Wiener amalgam space $(L^q,l^p)$ and contains the Lebesgue space $L^{α}$. We study the closure $(L^q,l^p)^{α}_{c,0}$ in $(L^q,l^p)^{α}$ of the space of test functions (infinitely differentiable and with compact support in $ℝ^d$) and obtain norm inequalities for Riesz potential operators and Riesz transforms in these spaces. We also introduce the Sobolev type space $W¹((L^q,l^p)^{α})$ (a subspace of a Morrey-Sobolev space, but a superspace of the classical Sobolev space $W^{1,α}$) and obtain in it Sobolev inequalities and a Kondrashov-Rellich compactness theorem.

Détail

Publié le : 2013-01-01

Zbl 1275.42034

EUDML-ID : urn:eudml:doc:280617