To the Sobolev embedding theorem for the limiting exponent
Informatics and Automation, Function spaces and related problems of analysis, Tome 284 (2014), pp. 89-104.

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We establish embeddings of the Sobolev space $W_p^s$ and the space $B_{pq}^s$ (with the limiting exponent) in certain spaces of locally integrable functions of zero smoothness. This refines the embedding of the Sobolev space in the Lorentz and Lorentz–Zygmund spaces. Similar problems are considered for the case of irregular domains and for the potential space.
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     title = {To the {Sobolev} embedding theorem for the limiting exponent},
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O. V. Besov. To the Sobolev embedding theorem for the limiting exponent. Informatics and Automation, Function spaces and related problems of analysis, Tome 284 (2014), pp. 89-104. http://geodesic.mathdoc.fr/item/TRSPY_2014_284_a4/

[1] Besov O.V., “O prostranstvakh funktsii nulevoi gladkosti”, Mat. sb., 203:8 (2012), 3–16 | DOI | MR | Zbl

[2] John F., Nirenberg L., “On functions of bounded mean oscillation”, Commun. Pure Appl. Math., 14 (1961), 415–426 | DOI | MR | Zbl

[3] Besov O.V., Ilin V.P., Nikolskii S.M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1996 | MR

[4] Kolyada V.I., “O sootnosheniyakh mezhdu modulyami nepreryvnosti v raznykh metrikakh”, Tr. MIAN, 181, 1988, 117–136 | MR

[5] O'Neil R., “Convolution operators and $L(p,q)$ spaces”, Duke Math. J., 30 (1963), 129–142 | DOI | MR | Zbl

[6] Peetre J., “Espaces d'interpolation et théorème de Soboleff”, Ann. Inst. Fourier., 16:1 (1966), 279–317 | DOI | MR | Zbl

[7] Yudovich V.I., “O nekotorykh otsenkakh, svyazannykh s integralnymi operatorami i resheniyami ellipticheskikh uravnenii”, DAN SSSR, 138:4 (1961), 805–808 | Zbl

[8] Hansson K., “Imbedding theorems of Sobolev type in potential theory”, Math. Scand., 45 (1979), 77–102 | MR | Zbl

[9] Brézis H., Wainger S., “A note on limiting cases of Sobolev embeddings and convolution inequalities”, Commun. Partial Diff. Eqns., 5:7 (1980), 773–789 | DOI | MR | Zbl

[10] Cianchi A., “Optimal Orlicz–Sobolev embeddings”, Rev. Mat. Iberoamer., 20:2 (2004), 427–474 | DOI | MR | Zbl

[11] Babichev D.S., Teoremy vlozheniya anizotropnykh prostranstv Soboleva v prostranstva nulevoi gladkosti, Dipl. rab., MFTI, Dolgoprudnyi, 2012

[12] Labutin D.A., “Neuluchshaemost neravenstv Soboleva dlya klassa neregulyarnykh oblastei”, Tr. MIAN, 232, 2001, 218–222 | MR | Zbl

[13] Kantorovich L.V., Akilov G.P., Funktsionalnyi analiz, Nauka, M., 1984 | MR | Zbl

[14] Besov O.V., “Integralnye otsenki differentsiruemykh funktsii na neregulyarnykh oblastyakh”, Mat. sb., 201:12 (2010), 69–82 | DOI | MR