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

• Autorzy: Mouhamadou Dosso , Ibrahim Fofana , Moumine Sanogo
• Języki publikacji: EN

Abstrakty

EN

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 𝓓 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.

Kategorie tematyczne

• 35C15: Integral representations of solutions
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 46B50: Compactness in Banach (or normed) spaces
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)
• 35F05: Linear first-order equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2013
• Tom: 108
• Numer: 2
• Strony: 133-153

Daty

wydano

2013

Twórcy

autor

Mouhamadou Dosso

• UFR de Mathématiques et Informatique, Université de Cocody, 22 BP 582 Abidjan, Côte d'Ivoire

autor

Ibrahim Fofana

• UFR de Mathématiques et Informatique, Université de Cocody, 22 BP 582 Abidjan, Côte d'Ivoire

autor

Moumine Sanogo

• D.E.R. de Mathématiques et Informatique, Université de Bamako, Bamako, Mali

Identyfikatory

DOI

10.4064/ap108-2-2