Local-to-global results in variable exponent spaces

Abstract

In this article a new method for moving from local to global results in variable exponent function spaces is presented. Several applications of the method are also given: Sobolev and trace embeddings; variable Riesz potential estimates; and maximal function inequalities in Morrey spaces are derived for unbounded domains. c International Press 2009. Non-standard growth, variable exponent, Lebesgue space, Sobolev space, Morrey space, Maximal operator, Riesz potential, Sobolev embedding, Hardy inequality, trace embedding. © International Press 2009.