Optimal embeddings of critical Sobolev–Lorentz–Zygmund spaces

Hidemitsu Wadade
2014 Studia Mathematica  
In this paper, we establish the embedding on the critical Sobolev-Lorentz-Zygmund space H n p p,q,λ1,··· ,λm (R n ) into the generalized Morrey space M Φ,r (R n ) with an optimal Young function Φ. Furthermore, as an application of this embedding, we obtain the almost Lipschitz continuity for functions in H n p +1 p,q,λ1,··· ,λm (R n ). O'Neil's inequality and its reverse play an essential role for the proof of main theorems. 2000 Mathematics Subject Classification. Primary 46E35 ; Secondary 26D10.
more » ... E35 ; Secondary 26D10.
doi:10.4064/sm223-1-5 fatcat:uwvkalkgivamnlo66iywx77cve