| Title:
|
Remarks on inequalities of Poincaré type (English) |
| Author:
|
Brown, Richard |
| Author:
|
Edmunds, David |
| Author:
|
Rákosník, Jiří |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
45 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
351-377 |
| . |
| Category:
|
math |
| . |
| MSC:
|
26D10 |
| MSC:
|
46E30 |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 0846.46022 |
| idMR:
|
MR1331472 |
| DOI:
|
10.21136/CMJ.1995.128530 |
| . |
| Date available:
|
2009-09-24T09:48:09Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128530 |
| . |
| Reference:
|
[1] C. J. Amick: Some remarks on Rellich’s theorem and the Poincaré inequality.J. London Math. Soc. (2) 18 (1978), 81–93. Zbl 0391.46029, MR 0502660, 10.1112/jlms/s2-18.1.81 |
| Reference:
|
[2] C. Bennett and R. Sharpley: Interpolation of Operators.Academic Press, Inc., Boston-San Diego-New York-Berkeley-London-Sydney-Tokyo-Toronto, 1988. MR 0928802 |
| Reference:
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[3] R. C. Brown and D. B. Hinton: Weighted interpolation inequalities and embeddings in $\mathbb{R}^N$.Canad. J. Math. 42 (1990), 959–980. MR 1099452, 10.4153/CJM-1990-051-8 |
| Reference:
|
[4] R. C. Brown and D. B. Hinton: A weighted Hardy’s inequality and nonoscillatory differential equations.Quaestiones Math. 15 (1992), 197–212. MR 1185887, 10.1080/16073606.1992.9631684 |
| Reference:
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[5] R. C. Brown and D. B. Hinton: An interpolation inequality and applications, Inequalities and Applications.R. P. Agarwal (ed.), World Scientific, Singapore-New Jersey-London-Hong Kong, 1994, pp. 87–101. MR 1299547 |
| Reference:
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[6] R. C. Brown and B. Opic: Embeddings of weighted Sobolev spaces into spaces of continuous functions.Proc. Roy. Soc. Lond. Ser. A 439 (1992), 279–296. MR 1193004, 10.1098/rspa.1992.0150 |
| Reference:
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[7] D. E. Edmunds and W. D. Evans: Spectral Theory and Differential Operators.Oxford University Press, Oxford, UK, 1987. MR 0929030 |
| Reference:
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[8] D. E. Edmunds and R. Hurri: Weighted Poincaré inequalities and Minkowski content.Proc. Roy. Soc. Edinburgh (to appear). |
| Reference:
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[9] D. E. Edmunds and B. Opic: Weighted Poincaré and Friedrichs inequalities.J. London Math. Soc. (2) 47 (1993), 79–96. MR 1200980, 10.1112/jlms/s2-47.1.79 |
| Reference:
|
[10] D. E. Edmunds, B. Opic and L. Pick: Poincaré and Friedrichs inequalities in abstract Sobolev spaces.Math. Proc. Cambridge Philos. Soc. 113 (1993), 355–379. MR 1198418, 10.1017/S0305004100076027 |
| Reference:
|
[11] D. E. Edmunds, B. Opic and J. Rákosník: Poincaré and Friedrichs inequalities in abstract Sobolev spaces II.Math. Proc. Cambridge Philos. Soc. 115 (1994), 159–173. MR 1253290, 10.1017/S0305004100071991 |
| Reference:
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[12] D. B. Hinton and R. Lewis: Singular differential operators with spectra discrete and bounded below.Proc. Roy. Soc. Edinburgh 84A (1979), 117–134. MR 0549875 |
| Reference:
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[13] A. Kufner, O. John and S. Fučík: Function Spaces.Academia, Prague and Noordhoff International Publishing, 1977. MR 0482102 |
| Reference:
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[14] W. A. J. Luxemburg: Banach Function Spaces.Thesis, Technische Hogeschool te Delft, 1955. Zbl 0068.09204, MR 0072440 |
| Reference:
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[15] O. Martio and M. Vuorinen: Whitney cubes, $p$-capacity, and Minkowski content.Exposition. Math. 5 (1987), 17–40. MR 0880256 |
| Reference:
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[16] M. A. Naimark: Linear Differential Operators, Part II.Frederick Ungar, New York, 1968. Zbl 0227.34020, MR 0262880 |
| Reference:
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[17] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague and Masson, Paris, 1967. MR 0227584 |
| Reference:
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[18] B. Opic and A. Kufner: Hardy-type Inequalities.Longman Scientific and Technical, Harlow, Essex, UK, 1990. MR 1069756 |
| Reference:
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[19] E. M. Stein: Singular Integrals and Differentiability Properties of Functions.Princeton University Press, Princeton, 1970. Zbl 0207.13501, MR 0290095 |
| Reference:
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[20] W. Ziemer: Weakly Differentiable Functions.Springer-Verlag, Berlin-New York, 1989. Zbl 0692.46022, MR 1014685 |
| . |
