Optimal embeddings of critical Sobolev-Lorentz-Zygmund spaces

• Autorzy: Hidemitsu Wadade
• Języki publikacji: EN

Abstrakty

EN

We establish the embedding of the critical Sobolev-Lorentz-Zygmund space $H^{n/p}_{p,q,λ₁,...,λₘ}(ℝⁿ)$ into the generalized Morrey space $ℳ_{Φ,r}(ℝⁿ)$ with an optimal Young function Φ. As an application, we obtain the almost Lipschitz continuity for functions in $H^{n/p + 1}_{p,q,λ₁,...,λₘ}(ℝⁿ)$. O'Neil's inequality and its reverse play an essential role in the proofs of the main theorems.

Kategorie tematyczne

• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 26D10: Inequalities involving derivatives and differential and integral operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 223
• Numer: 1
• Strony: 77-95

Daty

wydano

2014

Twórcy

autor

Hidemitsu Wadade

• Faculty of Mechanical Engineering, Institute of Science and Engineering, Kanazawa University, Kakuma-machi, Kanazawa-shi, Ishikawa-ken, 920-1192, Japan

Identyfikatory

DOI

10.4064/sm223-1-5