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Norms of embeddings of logarithmic Bessel potential spaces |
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| Authors: | David E. Edmunds Petr Gurka Bohumí r Opic |
| Affiliation: | Centre for Mathematical Analysis and its Applications, University of Sussex, Falmer, Brighton BN1 9QH, England ; Department of Mathematics, Czech University of Agriculture, 16521 Prague 6, Czech Republic ; Mathematical Institute, Academy of Sciences of the Czech Republic, Zitná 25, 11567 Prague 1, Czech Republic |
| Abstract: | Let  be a subset of  with finite volume, let  and let  be a Young function with  for large  . We show that the norm on the Orlicz space  is equivalent to
We also obtain estimates of the norms of the embeddings of certain logarithmic Bessel potential spaces in |
| Keywords: | Generalized Lorentz-Zygmund spaces logarithmic Bessel potential spaces Orlicz spaces of double and single exponential types equivalent norms embeddings |
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which are sharp in their dependences on 
provided that 
is large enough.