Optimal Embeddings of Spaces of Generalized Smoothness in the Critical Case |
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Authors: | Susana D Moura J??lio S Neves Cornelia Schneider |
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Institution: | (1) Mathematisches Institut, Friedrich-Schiller-Universit?t Jena, Ernst-Abbe-Platz 2, 07743 Jena, Germany;(2) Faculty of Mathematics and Computer Science, Adam Mickiewicz University Poznań, Ul. Umultowska 87, 61-614 Poznań, Poland |
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Abstract: | We study necessary and sufficient conditions for embeddings of Besov and Triebel-Lizorkin spaces of generalized smoothness
B(n/p,Y)p,q(\mathbbRn)B^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}) and
F(n/p,Y)p,q(\mathbbRn)F^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}), respectively, into generalized H?lder spaces
L¥,rm(·)( \mathbb Rn)\Lambda_{\infty,r}^{\mu(\cdot)}(\ensuremath {\ensuremath {\mathbb {R}}^{n}}). In particular, we are able to characterize optimal embeddings for this class of spaces provided q>1. These results improve the embedding assertions given by the continuity envelopes of
B(n/p,Y)p,q(\mathbbRn)B^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}) and
F(n/p,Y)p,q(\mathbbRn)F^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}), which were obtained recently solving an open problem of D.D. Haroske in the classical setting. |
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