Geodesic
Optimal embeddings of critical Sobolev–Lorentz–Zygmund spaces
Hidemitsu Wadade1
1Faculty of Mechanical Engineering Institute of Science and Engineering Kanazawa University Kakuma-machi, Kanazawa-shi Ishikawa-ken, 920-1192, Japan
Studia Mathematica, Tome 223 (2014) no. 1, pp. 77-95
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm223-1-5
Keywords: establish embedding critical sobolev lorentz zygmund space lambda ldots lambda mathbb generalized morrey space cal varphi mathbb optimal young function varphi application obtain almost lipschitz continuity functions lambda ldots lambda mathbb oneils inequality its reverse play essential role proofs main theorems

Hidemitsu Wadade  1

1 Faculty of Mechanical Engineering Institute of Science and Engineering Kanazawa University Kakuma-machi, Kanazawa-shi Ishikawa-ken, 920-1192, Japan 
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Hidemitsu Wadade. Optimal embeddings of
 critical Sobolev–Lorentz–Zygmund spaces. Studia Mathematica, Tome 223 (2014) no. 1, pp. 77-95. doi: 10.4064/sm223-1-5

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