An embedding theorem for Sobolev type functions with gradients in a Lorentz space

• Autorzy: Alireza Ranjbar-Motlagh
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.

Kategorie tematyczne

• 26B30: Absolutely continuous functions, functions of bounded variation
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 26D10: Inequalities involving derivatives and differential and integral operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 191
• Numer: 1
• Strony: 1-9

Daty

wydano

2009

Twórcy

autor

Alireza Ranjbar-Motlagh

• Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11365-9415, Tehran, Iran

Identyfikatory

DOI

10.4064/sm191-1-1