Norms of embeddings

of logarithmic Bessel potential spaces

Authors:
David E. Edmunds, Petr Gurka and Bohumír Opic

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2417-2425

MSC (1991):
Primary 46E35, 46E30

DOI:
https://doi.org/10.1090/S0002-9939-98-04327-5

MathSciNet review:
1451796

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Abstract | References | Similar Articles | Additional Information

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 which are sharp in their dependences on provided that is large enough.

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Additional Information

**David E. Edmunds**

Affiliation:
Centre for Mathematical Analysis and its Applications, University of Sussex, Falmer, Brighton BN1 9QH, England

Email:
d.e.edmunds@sussex.ac.uk

**Petr Gurka**

Affiliation:
Department of Mathematics, Czech University of Agriculture, 16521 Prague 6, Czech Republic

Email:
gurka@tf.czu.cz

**Bohumír Opic**

Affiliation:
Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 11567 Prague 1, Czech Republic

Email:
opic@math.cas.cz

DOI:
https://doi.org/10.1090/S0002-9939-98-04327-5

Keywords:
Generalized Lorentz-Zygmund spaces,
logarithmic Bessel potential spaces,
Orlicz spaces of double and single exponential types,
equivalent norms,
embeddings

Received by editor(s):
January 23, 1997

Additional Notes:
This research was partially supported by grant no. 201/94/1066 of the Grant Agency of the Czech Republic and by NATO Collaborative Research Grant no. CRG 930358; the research of the second author was also partially supported by EPSRC grant no. GR/L02937.

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1998
American Mathematical Society