Edmunds, David E.; Gurka, Petr; Opic, Bohumír Sharpness of embeddings in logarithmic Bessel-potential spaces. (English) Zbl 0860.46024 Proc. R. Soc. Edinb., Sect. A 126, No. 5, 995-1009 (1996). Summary: This paper is a continuation of [Stud. Math. 115, No. 2, 151-181 (1995; Zbl 0829.47024)], where embeddings of certain logarithmic Bessel-potential spaces (modelled upon generalized Lorentz-Zygmund spaces) in appropriate Orlicz spaces (with Young functions of single and double exponential type) were derived. The aim of this paper is to show that these embedding results are sharp in the sense of [J. A. Hempel, G. R. Morris and N. S. Trudinger, Bull. Aust. Math. Soc. 3, 369-373 (1970; Zbl 0205.12801)]. Cited in 27 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 47B38 Linear operators on function spaces (general) Keywords:logarithmic Bessel-potential spaces; Lorentz-Zygmund spaces; Orlicz spaces; Young functions of single and double exponential type Citations:Zbl 0829.47024; Zbl 0205.12801 PDFBibTeX XMLCite \textit{D. E. Edmunds} et al., Proc. R. Soc. Edinb., Sect. A, Math. 126, No. 5, 995--1009 (1996; Zbl 0860.46024) Full Text: DOI References: [1] Edmunds, Studia Math. 115 pp 151– (1995) [2] Bennett, Interpolation of Operators 129 (1988) · doi:10.1016/S0079-8169(08)60845-4 [3] Bennett, Dissertationes Math. 175 pp 1– (1980) [4] DOI: 10.2307/1971445 · Zbl 0672.31008 · doi:10.2307/1971445 [5] DOI: 10.1007/978-1-4612-1015-3 · Zbl 0692.46022 · doi:10.1007/978-1-4612-1015-3 [6] Trudinger, J. Math. Mech. 17 pp 473– (1967) [7] Edmunds, Houston J. Math. 21 pp 119– (1995) [8] DOI: 10.1512/iumj.1971.20.20101 · doi:10.1512/iumj.1971.20.20101 [9] Kufner, Function spaces (1977) [10] Lorentz, Pacific J. Math. 1 pp 411– (1951) · Zbl 0043.11302 · doi:10.2140/pjm.1951.1.411 [11] DOI: 10.1017/S0004972700046074 · Zbl 0205.12801 · doi:10.1017/S0004972700046074 [12] Fuglede, Mat. Fys. Medd. Dan. Vid. Selsk. 33 pp 1– (1960) [13] Stein, Singular Integrals and Differentiability Properties of Functions (1970) · Zbl 0207.13501 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.