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| In this talk, we consider the embedding on the critical Sobolev-Lorentz-Zygmund type space $H^{\frac{n}{p}}_{p,q,\lambda_1,\cdots,\lambda_m}(\Bbb R^n)$
into the generalized Morrey space ${\cal M}_{\Phi,r}(\Bbb R^n)$ with an optimal Young function $\Phi$. Furthermore, as an application of this embedding, we obtain the almost Lipschitz continuity for functions in $H^{\frac{n}{p}+1}_{p,q,\lambda_1,\cdots,\lambda_m}(\Bbb R^n)$.
O'Neil's inequality and its reverse play an essential role for the proof of main theorems. |
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