Optimal Orlicz domains in Sobolev embeddings into Marcinkiewicz spaces

2016/02/01 by Vít Musil
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Computer science #Domain (mathematical analysis) #Embedding #Functional analysis #Interpolation space #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Omega #Physics #Pure mathematics #Sobolev space #Space (punctuation) #TRACE (psycholinguistics) #math.FA

paper · pdf · doi:10.1016/j.jfa.2016.01.019

published as J. Funct. Anal. 270 (2016), no. 7, 2653-2690 · 27 pages

openalex publication_date 2016/02/01 · arxiv created 2019/12/08 · arxiv updated 2019/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper we present a method for determining whether there exists a largest Orlicz space L^A(Ω) satisfying the Sobolev embedding W^mL^A(Ω) → Y(Ω) where Y(Ω) stands for an arbitrary so-called Marcinkiewicz endpoint space. The tool developed in this work enables us to investigate the optimality of Orlicz domain spaces in Sobolev embeddings and also in Sobolev trace embeddings on domains Ω in ℝⁿ with various regularity.

Citations

• Logarithmic Sobolev Inequalities
• Sobolev Spaces