Optimal embeddings of critical Sobolev-Lorentz-Zygmund spaces

Hidemitsu Wadade

Studia Mathematica, Tome 223 (2014), p. 77-95 / Harvested from The Polish Digital Mathematics Library

Résumé

We establish the embedding of the critical Sobolev-Lorentz-Zygmund space $H_{p, q, λ ₁, . . ., λ ₘ}^{n / p} (ℝ ⁿ)$ into the generalized Morrey space $ℳ_{Φ, r} (ℝ ⁿ)$ with an optimal Young function Φ. As an application, we obtain the almost Lipschitz continuity for functions in $H_{p, q, λ ₁, . . ., λ ₘ}^{n / p + 1} (ℝ ⁿ)$ . O’Neil’s inequality and its reverse play an essential role in the proofs of the main theorems.

Publié le : 2014-01-01

Zbl 1317.46024

EUDML-ID : urn:eudml:doc:285381

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     title = {Optimal embeddings of critical Sobolev-Lorentz-Zygmund spaces},
     journal = {Studia Mathematica},
     volume = {223},
     year = {2014},
     pages = {77-95},
     zbl = {1317.46024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-1-5}
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Hidemitsu Wadade. Optimal embeddings of critical Sobolev-Lorentz-Zygmund spaces. Studia Mathematica, Tome 223 (2014) pp. 77-95. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-1-5/