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

Volume 191 / 2009

Alireza Ranjbar-Motlagh Studia Mathematica 191 (2009), 1-9 MSC: Primary 26D10, 46E30; Secondary 46E35, 26B30. DOI: 10.4064/sm191-1-1

Abstract

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.

Authors

  • Alireza Ranjbar-MotlaghDepartment of Mathematical Sciences
    Sharif University of Technology
    P.O. Box 11365-9415
    Tehran, Iran
    e-mail

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