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

Tom 108 / 2013

Mouhamadou Dosso, Ibrahim Fofana, Moumine Sanogo Annales Polonici Mathematici 108 (2013), 133-153 MSC: Primary 42B20, 46B50, 46E35; Secondary 35C15, 35F05. DOI: 10.4064/ap108-2-2

Streszczenie

For $1\leq q\leq \alpha \leq p\leq \infty$, $(L^q,l^p)^{\alpha}$ is a complex Banach space which is continuously included in the Wiener amalgam space $(L^q,l^p)$ and contains the Lebesgue space $L^{\alpha}$.

We study the closure $(L^q,l^p)^{\alpha}_{c,0}$ in $(L^q,l^p)^{\alpha}$ of the space $\mathcal{D}$ of test functions (infinitely differentiable and with compact support in $\mathbb R^d$) and obtain norm inequalities for Riesz potential operators and Riesz transforms in these spaces. We also introduce the Sobolev type space $W^1((L^q,l^p)^{\alpha})$ (a subspace of a Morrey–Sobolev space, but a superspace of the classical Sobolev space $W^{1,\alpha}$) and obtain in it Sobolev inequalities and a Kondrashov–Rellich compactness theorem.

Autorzy

  • Mouhamadou DossoUFR de Mathématiques et Informatique
    Université de Cocody
    22 BP 582 Abidjan, Côte d'Ivoire
    e-mail
  • Ibrahim FofanaUFR de Mathématiques et Informatique
    Université de Cocody
    22 BP 582 Abidjan, Côte d'Ivoire
    e-mail
  • Moumine SanogoD.E.R. de Mathématiques et Informatique
    Université de Bamako
    Bamako, Mali
    e-mail

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