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Optimal embeddings of critical Sobolev–Lorentz–Zygmund spaces

Volume 223 / 2014

Hidemitsu Wadade Studia Mathematica 223 (2014), 77-95 MSC: Primary 46E35; Secondary 26D10. DOI: 10.4064/sm223-1-5

Abstract

We establish the embedding of the critical Sobolev–Lorentz–Zygmund space $H^{{n}/{p}}_{p,q,\lambda _1,\ldots ,\lambda _m}(\mathbb R^n)$ into the generalized Morrey space ${\cal M}_{\varPhi ,r}(\mathbb R^n)$ with an optimal Young function $\varPhi $. As an application, we obtain the almost Lipschitz continuity for functions in $H^{{n}/{p}+1}_{p,q,\lambda _1,\ldots ,\lambda _m}(\mathbb R^n)$. O'Neil's inequality and its reverse play an essential role in the proofs of the main theorems.

Authors

  • Hidemitsu WadadeFaculty of Mechanical Engineering
    Institute of Science and Engineering
    Kanazawa University
    Kakuma-machi, Kanazawa-shi
    Ishikawa-ken, 920-1192, Japan
    e-mail

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