Burenkov V. I. Compactness of embeddings for Sobolev and more general spaces and extensions with preservation of some smoothness, To appear.

Burenkov V. I.; dman M. L. Gol,’ 1979; On the extension of functions in $L_p$ (Russian). Trudy Mat. Inst. Steklov 150, (,))., 31–51; English transl.: Proc. Steklov Inst. Math. 150 (197,9 | MR 0544003

Burenkov V. I.; Kalyabin G. A. Lower estimates of the norms of extension operators for Sobolev spaces on the halfline, To appear in Math. Nachr. | MR 1784635 | Zbl 0986.46021

Rychkov V. S. On restrictions and extensions of Besov and Triebel-Lizorkin spaces with respect to Lipschitz domains, To appear. | MR 1721827

Whitney H. Analytic extension of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), 63–89. (1934) | MR 1501735

Hestenes M. R. Extension of the range of a differentiable function, Duke Math. J. 8 (1941), 183–192. (1941) | MR 0003434 | Zbl 0024.38602

Sobolev S. L. Applications of functional analysis in mathematical physics, 1st ed.: LGU, Leningrad 1950 (Russian). 2nd ed.: NGU, Novosibirsk 1963 (Russian). 3rd ed.: Nauka, Moscow 1988 (Russian). English translation of 3rd ed.: Translations of Mathematical Monographs, 90, Amer. Math. Soc., Providence, RI 1991. (1950) | MR 0165337

Babich V. M. On the extension of functions, (Russian). Uspekhi Mat. Nauk 8 (1953), 111–113. (1953) | MR 0056675

skii S. M. Nikol,’ On the solutions of the polyharmonic equation by a variational method, (Russian). Dokl. Akad. Nauk SSSR 88 (1953), 409–411. (1953)

Calderón A. P. Lebesgue spaces of differentiable functions and distributions, Proc. Sympos. Pure Math. IV (1961), 33–49. (1961) | MR 0143037 | Zbl 0195.41103

skii S. M. Nikol,’ On embedding, extension and approximation theorems for differentiable functions of several variables, (Russian). Uspekhi Mat. Nauk 16 (1961), 63–114; English transl.: Russian Math. Surveys 16 (1961). (1961)

Sobolev S. L.; skii S. M. Nikol,’ Embedding theorems, (Russian). Vol. 1, Proc. Fourth All-Union Math. Congress, 1961, Nauka, Leningrad 1963, 227–242; English transl.: Amer. Math. Soc. Transl. (2), 87 (1970). (1961) | MR 0171188

Seeley R. T. Extension of $C^{\infty }$-functions defined in halfspace, Proc. Amer. Math. Soc. 15 (1964), 625–626. (1964) | MR 0165392 | Zbl 0127.28403

Burenkov V. I. Embedding and extension theorems for classes of differentiable functions of several variables defined on the whole space, (Russian). Itogi Nauki i Tekhniki: Mat. Anal. 1965, VINITI, Moscow 1966, 71–155; English transl.: Progress in Math. 2, Plenum Press, 1968. (1965) | MR 0206698

Burenkov V. I. Some properties of classes of differentiable functions in connection with embedding and extension theorems, (Russian). Ph.D. thesis, Moscow, Steklov Math. Inst. (1966), 145 pp. (1966)

Burago; Yu. D.; ya V. G. Maz,’ Some problems of the potential theory and function theory for domains with irregular boundaries, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklov 3 (1967), 1–152 (Russia); English transl.: Seminars in Math., V. A. Steklov Math. Inst., Leningrad 3 (1969). (1967)

skii S. M. Nikol,’ Approximation of functions of several variables and embedding theorems, 1st ed., Nauka, Moscow 1969 (Russian); 2nd ed., Nauka, Moscow 1977 (Russian); English transl. of 1st ed., Springer-Verlag, Berlin 1975. (1969)

Besov O. V.; in V. P. Il,’ Kudryavtsev L. D.; Lizorkin P. I.; skii S. M. Nikol,’ Embedding theory for classes of differentiable functions of several variables, (Russian). Proc. Sympos. in honour of the 60th birthday of academician S. L. Sobolev, Inst. Mat. Sibirsk. Otdel. Akad. Nauk. SSSR, Nauka, Moscow 1970, 38–63. (1970)

Stein E. M. Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton 1970. (1970) | MR 0290095 | Zbl 0207.13501

Burenkov V. I. On regularized distance, (Russian). Trudy MIREA. Issue 67. Mathematics (1973), 113–117. (1973) | MR 0499023

Burenkov V. I. On the density of infinitely differentiable functions in Sobolev spaces for an arbitrary open set, (Russian). Trudy Mat. Inst. Steklov 131 (1974), 39–50; English transl.: Proc. Steklov Inst. Math. 131 (1974). (1974) | MR 0367642 | Zbl 0313.46033

Sobolev S. L. Introduction to the theory of cubature formulae, (Russian). Nauka, Moscow 1974. (1974) | MR 0478560

Adams R. A. Sobolev spaces, Academic Press, New York 1975. (1975) | MR 0450957 | Zbl 0314.46030

Besov O. V.; in V. P. Il,’ skii S. M. Nikol,’ Integral representation of functions and embedding theorems, (Russian). 1st ed., Nauka, Moscow 1975; 2nd ed., Nauka, Moscow 1996 (Russian); English transl. of 1st ed., Vols. 1, 2, Wiley, 1979. (1975) | MR 0430771

Burenkov V. I. On the extension of functions with preservation and with deterioration of the differential properties, (Russian). Dokl. Akad. Nauk SSSR 224 (1975), 269–272; English transl.: Soviet Math. Dokl. 16 (1975). (1975) | MR 0405083 | Zbl 0351.46022

Burenkov V. I.; Fain B. L. On the extension of functions in Sobolev spaces from a strip with deteriorations of class, (Russian). Deposited in VINITY Ac. Sci. USSR, No 2511–74 (1975), 12 pp. (1975)

Burenkov V. I. On a certain method for extending differentiable functions, (Russian). Trudy Mat. Inst. Steklov 140 (1976), 27–67; English transl.: Proc. Steklov Inst. Math. 140 (1976). (1976)

Burenkov V. I. On the extension of functions with preservation of semi-norm, (Russian). Dokl. Akad. Nauk SSSR 228 (1976), 779–782; English transl.: Soviet Math. Dokl. 17 (1976). (1976) | MR 0412796

Burenkov V. I.; Fain B. L. On the extension of functions in anisotropic spaces with preservation of class, (Russian). Dokl. Akad. Nauk SSSR 228 (1976), 525–528; English transl.: Soviet Math. Dokl. 17 (1976). (1976) | MR 0410359

Fain B. L. The extension of functions from an infinite cylinder, (Russian). Trudy Mat. Inst. Steklov 140 (1976), 277–284; English transl.: Proc. Steklov Inst. Math. J. 140 (1979). (1976) | MR 0626997 | Zbl 0397.46026

Kufner A.; John O.; Fučík S. Function spaces, Academia, Prague & Noordhoff International Publishing, Leyden 1977. (1977) | MR 0482102

Burenkov V. I. On partitions of unity, (Russian). Trudy Mat. Inst. Steklov 150 (1979), 24–30; English transl.: Proc. Steklov Inst. Math. 150 (1979). (1979) | MR 0544002 | Zbl 0417.46036

Burenkov V. I.; Fain B. L. On the extension of functions in anisotropic classes with preservation of the class, (Russian). Trudy Mat. Inst. Steklov 150 (1979), 52–66; English transl.: Proc. Steklov Inst. Math. 150 (1979). (1979) | MR 0544004

yanov S. K. Vodop,’ dshtein V. M. Gol,’ Latfullin T. G. A criterion for extension of functions in class $L_2^1$ from unbounded planar domains, (Russian). Sibirsk. Mat. Zh. 34 (1979), 416–419; English transl.: Siberian Math. J. 34 (1979). (1979)

yanov S. K. Vodop,’ dshtein V. M. Gol,’ Reshetnyak; Yu. G. On geometric properties of functions with first generalized derivatives, (Russian). Uspekhi Mat. Nauk 34 (1979), no. 1(205), 3–74; English transl.: Russian Math. Surveys 20 (1985). (1979)

dshtein V. M. Gol,’ Extension of functions with first generalized derivatives from planar domains, (Russian). Dokl. Akad. Nauk SSSR 257 (1981), 268–271; English transl.: Soviet Math. Dokl. 23 (1981). (1981) | MR 0610166

Jones P. W. Quasiconformal mappings and extendability of functions in Sobolev spaces, Acta Math. 147 (1981), 71–88. (1981) | MR 0631089 | Zbl 0489.30017

Burenkov V. I. Investigation of spaces of differentiable functions with irregular domain, (Russian). D.Sc. thesis, Steklov Math. Inst., Moscow 1982, 312 pp. (1982)

dshtein V. M. Gol,’ Sitnikov V. N. On extension of functions in the class $W_p^1$ across Hölder boundaries, (Russian). In “Embedding theorems and their applications”. Trudy Semin. S. L. Sobolev, Novosibirsk 1 (1982), 31–43. (1982)

dshtein V. M. Gol,’ Reshetnyak; Yu. G. Foundations of the theory of functions with generalized derivatives and quasiconformal mappings, (Russian). Nauka, Moscow 1983; English transl.: Reidel, Dordrecht 1989. (1983) | MR 0738784

dshtein V. M. Gol,’ yanov S. K. Vodop,’ Prolongement des fonctions de classe $L_p^1$ et applications quasiconformes, C. R. Acad Sci. Paris Sér. A 290 (1983), 453–456. (1983)

Triebel H. Theory of function spaces, Birkhäuser, Basel 1983; and Akad. Verlag. Geest & Portig, Leipzig 1983. (1983) | MR 0781540 | Zbl 0546.46028

Burenkov V. I. On estimates of the norms of extension operators, (Russian). 9-th All-Union school on the theory of operators in function spaces. Ternopol. Abstracts (1984), 19–20. (1984)

ya V. G. Maz,’ Sobolev spaces, (Russian). LGU, Leningrad 1984; English transl.: Springer-Verlag, Springer Series in Soviet Mathematics, Berlin 1985. (1984) | MR 0807364

ya V. G. Maz,’ Poborchii S. V. On extension of functions in Sobolev spaces to the exterior of a domain with a peak vertex on the boundary, (Russian). Dokl. Akad. Nauk SSSR 275 (1984), 1066–1069; English transl.: Soviet Math. Dokl. 29 (1984). (1984) | MR 0745847

Uspenskii S. V.; Demidenko G. V.; Perepelkin V. G. Embedding theorems and their applications to differential equations, (Russian). Nauka, Novosibirsk 1984. (1984)

Burenkov V. I. Extension of functions with preservation of Sobolev semi-norm, (Russian). Trudy Mat. Inst. Steklov 172 (1985), 81–95; English transl.: Proc. Steklov Inst. Math. 172 (1985). (1985) | MR 0810420

Fain B. L. On extension of functions in Sobolev spaces for irregular domains with preservation of the smoothness exponent, (Russian). Dokl. Akad. Nauk SSSR 285 (1985), 296–301; English transl.: Soviet Math. Dokl. 30 (1985). (1985) | MR 0820855

Kufner A. Weighted Sobolev spaces, John Wiley and Sons, Chichester 1985. (1985) | MR 0802206 | Zbl 0579.35021

Burenkov V. I. On sharp constants in the inequalities for the norms of intermediate derivatives on a finite interval, II, (Russian). Trudy Mat. Inst. Steklov 173 (1986), 38–49; English transl.: Proc. Steklov Inst. Math. 173 (1986). (1986) | MR 0864833

Burenkov V. I.; Popova E. M. On improving extension operators with the help of the operators of approximation with preservation of the boundary values, (Russian). Trudy Mat. Inst. Steklov 173 (1986), 50–54; English transl.: Proc. Steklov Inst. Math. 173 (1986). (1986) | MR 0864834

Konovalov V. N. A criterion for extension of Sobolev spaces $W_{\infty }^{\left(r\right)}$ on bounded planar domains, (Russian). Dokl. Akad. Nauk SSSR 289 (1986), 36–39; English transl.: Soviet Math. Dokl. 33 (1986). (1986) | MR 0852285

ya V. G. Maz,’ Poborchii S. V. Extension of functions in Sobolev spaces to the exterior of a domain with a peak vertex on the boundary I, (Russian). Czechoslovak Math. J. 36 (1986), 634–661. (1986) | MR 0863193

ya V. G. Maz,’ Poborchii S. V. Extension of functions in Sobolev spaces to the exterior of a domain with a peak vertex on the boundary II, (Russian). Czechoslovak Math. J. 37 (1987), 128–150. (1987) | MR 0875135

Kudryavtsev L. D.; skii S. M. Nikol,’ Spaces of differentiable functions of several variables and the embedding theorems, (Russian). Contemporary problems in mathematics. Fundamental directions. V. 26 (1988). Analysis – 3. VINITI, Moscow, 5–157. (1988) | MR 1178111

Ziemer W. P. Weakly differentiable functions, Springer-Verlag, New York 1989. (1989) | MR 1014685 | Zbl 0692.46022

Chua S. K. Extension theorems on weighted Sobolev spaces, Indiana. Univ. Math. 117 (1992), 1027–1076. (1992) | MR 1206339 | Zbl 0767.46025

Herron D. A.; Koskela P. Uniform and Sobolev extension domains, Proc. Amer. Math. Soc. 114, 2 (1992), 483–489. (1992) | MR 1075947 | Zbl 0757.30022

Popova E. M. On improving extension operators with the help of the operators of approximation with preservation of the boundary values, (Russian). In: “Function spaces and applications to differential equations”, Peoples’ Friendship University of Russia, Moscow (1992), 154–165. (1992)

Triebel H. Theory of function spaces. II, Birkhäuser, Basel 1992. (1992) | MR 1163193 | Zbl 0763.46025

Burenkov V. I.; Gorbunov A. L. Sharp estimates for the minimal norm of an extension operator for Sobolev spaces, (Russian). Dokl. Akad. Nauk SSSR 330 (1993), 680–682; English transl.: Soviet Math. Dokl. 47 (1993). (1993) | MR 1242163

Zobin N. Whitney’s problem: extendability of functions and intrinsic metric, C. R. Acad. Sci. Paris 320, 1 (1995), 781–786. (1995) | MR 1326682 | Zbl 0826.46017

Garofalo N.; Nhieu D. M. Lipschitz continuity, global smoothness approximation and extension theorems for Sobolev functions in Carnot-Carathéodory spaces, Preprint, Purdue Univ. (1996). (1996) | MR 1631642

Kalyabin G. A. The least norm estimates for certain extension operators from convex planar domains, In: Conference in Mathematical Analysis and Applications in Honour of L. I. Hedberg’s Sixtieth Birthday. Abstracts. Linköping 1996, pp. 55–56. (1996)

ya V. G. Maz,’ Poborchii S. V. Extension of functions in Sobolev spaces on parameter dependent domains, Math. Nachr. 178 (1996), 5–41. (1996) | MR 1380702

Burenkov V. I.; Gorbunov A. L. Sharp estimates for the minimal norm of an extension operator for Sobolev spaces, (Russian). Izv. Ross. Akad. Nauk Ser. Mat. 61 (1997), 1–44. (1997) | MR 1440311

Lieb E. H.; Loss M. Analysis, Amer. Math. Soc. 1997. (1997)

ya V. G. Maz,’ Poborchii S. V. Differentiable functions on bad domains, World Scientific Publishing, Singapore 1997. (1997) | MR 1643072

Burenkov V. I. Extension theorems for Sobolev spaces, In: Proc. of the conference “Functional analysis, partial differential equations and applications” in honour of V. Maz’ya, held in Rostock, 31. 08.–4. 09. 1998 (to appear). (1998) | MR 1747873

Burenkov V. I. Sobolev spaces on domains, B.G. Teubner, Stuttgart 1998. (1998) | MR 1622690 | Zbl 0893.46024

Burenkov V. I.; Schulze B.-W.; Tarkhanov N. N. Extension operators for Sobolev spaces commuting with a given transform, Glasgow Math. J. 40 (1998), 291–296. (1998) | MR 1630199 | Zbl 0913.35160