×

Properties of functions in some weighted spaces. (English) Zbl 1081.46026

Summary: Differential properties of functions from weighted spaces \(S^r_{p,\alpha}W(\overset {+} E^n)\) with dominant mixed derivatives are investigated. For this reason, an integral identity for rather smooth and finite functions is derived and, with the help of this identity, imbedding theorems are proved.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Sobolev SL, American Mathematical Society (1950)
[2] Nikol’skii SM, Mathematical Review 61 pp 224– (1963)
[3] Besov OV, Integral representations of functions and imbedding theorems 11 (1979)
[4] Il’in VP, Proceedings of the Steklov Institute of Mathematics 64 pp 227– (1962)
[5] Dzhabrailov AD, Nauka pp pp. 73–75– (1970)
[6] Vasil’chuk MYu., Siberian Advances in Mathematics 7 pp 97– (1997)
[7] DOI: 10.1023/A:1017996900877 · Zbl 0885.31004 · doi:10.1023/A:1017996900877
[8] DOI: 10.1007/s003659900107 · Zbl 0926.41001 · doi:10.1007/s003659900107
[9] DOI: 10.1007/s002090100332 · Zbl 1055.35087 · doi:10.1007/s002090100332
[10] Kurokawa Takahide, RIMS Kokyuroku 1116 pp 107– (1999)
[11] Adzhiev SS, Proceedings of the Steklov Institute of Mathematics 214 pp 1– (1996)
[12] Kerimova GT, Baku pp p. 127– (1997)
[13] Kerimova GT, Journal of Science and Arts Faculty 4 pp 9– (1998)
[14] Kerimova GT, Journal of Science and Arts Faculty 4 pp 31– (1998)
[15] Dzhabrailov AD 2001 The properties of functions on the boundary surfaces (English), 3rd International ISAAC Congress Freie Univ. Berlin, Germany, August 20–25, 2001, Abstracts pp. 19–20
[16] Dzhabrailov AD, Izvestiya Akademii Nauk Azerbaidzhana. SSR, FTMN 4 pp 23– (1988)
[17] Alisoy GT, International Journal of Applied Mathematics 4 pp 371– (2002)
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.