| Popis: |
In this paper, the authors prove some Franke-Jawerth embedding for the Besov-type spaces B p , q s , ? ( R n ) and the Triebel-Lizorkin-type spaces F p , q s , ? ( R n ) . By using some limiting embedding properties of these spaces and the Besov-Morrey spaces N u , p , q s ( R n ) , the continuity envelopes in B p , q s , ? ( R n ) , F p , q s , ? ( R n ) and N u , p , q s ( R n ) are also worked out. As applications, the authors present some Hardy type inequalities in the scales of B p , q s , ? ( R n ) , F p , q s , ? ( R n ) and N u , p , q s ( R n ) , and also give the estimates for approximation numbers of the embeddings from B p , q s , ? ( ? ) , F p , q s , ? ( ? ) and N u , p , q s ( ? ) into C ( ? ) , where ? denotes the unit ball in R n . |
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