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Entropy and approximation numbers of limiting embeddings; an approach via Hardy inequalities and quadratic forms. (English) Zbl 1242.47018
Let B be the unit ball in n . The paper deals with the continuous embeddings of a special weighted Sobolev space of functions defined on B into the Lebesgue space of complex-valued measurable functions on B. The weights involve log-terms. In the case where the embeddings are compact, some two-sided estimates for the entropy numbers and approximation numbers are proved.
MSC:
47B06Riesz operators; eigenvalue distributions; approximation numbers, s-numbers etc.of operators
41A46Approximation by arbitrary nonlinear expressions; widths and entropy
47B38Operators on function spaces (general)
References:
[1]Davies, E. B.: Spectral theory and differential operators, (1995)
[2]Edmunds, D. E.; Evans, W. D.: Spectral theory and differential operators, (1987)
[3]Edmunds, D. E.; Evans, W. D.: Hardy operators, function spaces and embeddings, (2004)
[4]Edmunds, D. E.; Netrusov, Yu.: Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces, Studia math. 128, 71-102 (1998) · Zbl 0919.46024
[5]Edmunds, D. E.; Triebel, H.: Function spaces, entropy numbers, differential operators, (1996)
[6]Haroske, D. D.; Skrzypczak, L.: Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights I, Rev. mat. Complut. 21, 135-177 (2008) · Zbl 1202.46039
[7]Haroske, D. D.; Skrzypczak, L.: Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, II, Ann. acad. Sci. fenn. Math. 36, 111-138 (2011) · Zbl 1222.46027 · doi:10.5186/aasfm.2011.3607
[8]Haroske, D. D.; Skrzypczak, L.: Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases, J. funct. Spaces appl. 9, 129-178 (2011)
[9]Haroske, D. D.; Triebel, H.: Distributions, Sobolev spaces, elliptic equations, (2008)
[10]Kühn, Th.: Entropy numbers in sequence spaces with an application to weighted function spaces, J. approx. Theory 153, 40-52 (2008) · Zbl 1145.47017 · doi:10.1016/j.jat.2008.01.002
[11]Kufner, A.; Maligranda, L.; Persson, L. -E.: The Hardy inequality: about its history and some related results, (2007)
[12]Ma, Z. -M.; Röckner, M.: Introduction to the theory of non-symmetric Dirichlet forms, (1992) · Zbl 0826.31001
[13]Maz’ja, V. G.: Sobolev spaces, (1985)
[14]Opic, B.; Kufner, A.: Hardy-type inequalities, Pitman research notes in mathematics 219 (1990) · Zbl 0698.26007
[15]Triebel, H.: Higher analysis, (1992) · Zbl 0783.46001
[16]Triebel, H.: Relations between approximation numbers and entropy numbers, J. approx. Theory 78, 112-116 (1994) · Zbl 0811.47020 · doi:10.1006/jath.1994.1064
[17]Triebel, H.: The structure of functions, (2001)
[18]Triebel, H.: Theory of function spaces III, (2006)