References
S. M. Nikol'skii, “On a certain property of the classesH l p ,” Ann. Univ. Sci. Budapest, No. 3/4, 205–216 (1960/1961).
V. I. Burenkov, “Local lemmas for certain classes of differentiable functions,” Trudy Mat. Inst. Steklov. Akad. Nauk SSSR,77, 65–71 (1965).
V. I. Burenkov, “Additivity of the spacesW l p (Ω) andB l p (Ω), and embedding theorems for domains of general type,” Trudy Mat. Inst. Steklov. Akad. Nauk SSSR,105, 30–45 (1969).
V. I. Burenkov, “Additivity of the classesW l p (Ω),” Trudy Mat. Inst. Steklov. Akad. Nauk SSSR,89, 31–55 (1967).
V. I. Burenkov, “Additivity of the spacesW l p (Ω)” in: Embedding Theorems and Their Applications, Nauka, Moscow, 1970, pp. 47–52.
Yu. V. Kuznetsov, “Certain inequalities for fractional seminorms,” Trudy Mat. Inst. Steklov. Akad. Nauk SSSR,131, 147–157 (1974).
Yu. V. Kuznetsov, “On a certain property of the spacesW l p (Ω) andW l p,θ ,” in: Applications of the Methods of Functional Analysis and Computational Mathematics [in Russian], Novosibirsk (1975).
A. Ya. Rutitskaya, “Additivity of general function spaces,” submitted to VINITI, 1985, Voronezh. Lesotekhn. Inst., Voronezh, 1985, No. 1800–85.
A. Ya. Rutitskaya, Properties of Function Spaces over Domains with Nonsmooth Boundary and Their Applications, Diss. Kand. Fiz.-Mat. Nauk, Voronezh (1990).
V. I. Burenkov, “Certain properties of the classesW l p (Ω) andW l,l p for 0<l<1,” Trudy Mat. Inst. Steklov. Akad. Nauk SSSR,77, 72–88 (1965).
O. V. Besov and V. P. Il'in, “A natural extension of the class of domains in embedding theorems,” Mat. Sb.,75, No. 4, 483–495 (1968).
S. V. Uspenskii, G. V. Demidenko, and V. G. PerepËlkin, Embedding Theorems and Applications to Differential Equations [in Russian], Nauka, Novosibirsk (1984).
L. N. Slobodetskii, “Sobolev spaces of fractional order and their application to boundary value problems for partial differential equations,” Dokl. Akad. Nauk SSSR,118, No. 2, 243–246 (1958).
L. N. Slobodetskii, “Generalized Sobolev spaces and their application to boundary value problems for partial differential equations,” Uchen. Zap. Leningrad. Ped. Inst.,197, 54–112 (1958).
O. V. Besov, V. P. Il'in, and S. M. Nikol'skii, Integral Representations of Functions and Embedding Theorems [in Russian], Nauka, Moscow (1975).
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Translated fromSibirskii Matematicheskii Zhurnal, Vol. 35, No. 1, pp. 24–40, January–February, 1994.
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Burenkov, V.I., Senusi, A. Estimates for constants in additivity inequalities for function spaces. Sib Math J 35, 21–36 (1994). https://doi.org/10.1007/BF02104945
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DOI: https://doi.org/10.1007/BF02104945