It is known that in certain limiting cases, spaces of Sobolev type modelled upon Zygmund spaces are embedded in Orlicz spaces of exponential type. Estimates of the entropy numbers of such embeddings are studied.
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David E. Edmunds, Petr Gurka, Entropy Numbers of Limiting Embeddings of Logarithmic Sobolev Spaces into Exponential Spaces. Z. Anal. Anwend. 29 (2010), no. 2, pp. 235–250DOI 10.4171/ZAA/1407