Geodesic
Weighted Interpolation Inequalities and Embeddings in Rn
Canadian journal of mathematics, Tome 42 (1990) no. 6, pp. 959-980

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This paper is a continuation of [3] which initiated a systematic study of sufficient conditions for the weighted interpolation inequality of sum form, 1.1 to hold. Here φ, θ are non-negative functions of m, j, p, q, r, Ω is a bounded or unbounded domain in Rn, ∊ belongs to an interval Γ=(0, ∊ 0), u is in a certain Banach space E(Ω), and N, W, P are measurable real functions satisfying N≧ 0, W, P > 0, as well as additional conditions stated below. Finally the constant K does not depend on u although it may depend on the other parameters.
DOI : 10.4153/CJM-1990-051-8
Mots-clés : 26D10, 26D20, 54C25 
Brown, R. C.; Hinton, D. B. Weighted Interpolation Inequalities and Embeddings in Rn. Canadian journal of mathematics, Tome 42 (1990) no. 6, pp. 959-980. doi: 10.4153/CJM-1990-051-8
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[1] 1. Adams, R.A., “Sobolev Spaces,” Academic Press, New York, 1975. Google Scholar

[2] 2. Brown, R.C. and Hinton, D.B., Necessary and sufficient conditions for one variable weighted interpolation inequalities, J. London Math. Soc. (2)35 (1987), 439–453. Google Scholar

[3] 3. Brown, R.C. and Hinton, D.B., Weighted interpolation inequalities of sum and product form in Rn , Proc. London Math. Soc. (1988), 261–280. Google Scholar

[4] 4. Edmunds, D.E. and Evans, W.D., “Spectral Theory and Differential Operators,” Oxford University Press, 1987. Google Scholar

[5] 5. Evans, W.D., Kwong, N.K., and Zettl, A., Lower bounds for the spectrum of ordinary differential operators, J. Differential Eqs. (1983), 123-155. Google Scholar | DOI

[6] 6. Garcia-Cuerva, J. and Rubio De Francia, J., “Weighted norm inequalities and related topics,“ North Holland, Amsterdam, 1985. Google Scholar

[7] 7. Gurka, P. and Opic, B., Continuous and compact imbeddings of weighted Sobolev spaces I, Czech. Math. J. (1988), 611–617. Google Scholar

[8] 8. Gurka, P. and Opic, B., Continuous and compact imbeddings of weighted Sobolev spaces II, Czech. Math. J. 39 (1989), 78–94. Google Scholar

[9] 9. Gurka, P. and Opic, B., N-dimensional Hardy inequality and imbedding theorems for weightedSobolev spaces on unbounded domains. To appear in Proceedings, Summer School on Function Spaces, etc., Sodankyla, Finland. Google Scholar

[10] 10. Gutierrz, C.E. and Wheeden, R.L., Interpolation inequalities with weights, to appear. Google Scholar

[11] 11. Guzmann, Miguel De, Differentiation of Integrals in Rn , in “Lecture Notes in Mathematics 481,“ Springer, Berlin, 1975. Google Scholar | DOI

[12] 12. Kufner, A., “Weighted Sobolev Spaces,” John Wiley and Sons, Chichester, 1985. Google Scholar

[13] 13. Kufner, A., John, O., and Fucik, S., “Function Spaces,” Noordhoff International Publishing, Leyden, 1977. Google Scholar

[14] 14. Kwong, M.K. and Zettl, A., Ramifications of Landau's inequality, Proc. Roy. Soc. Edinburgh A86(1980), 175-212. Google Scholar

[15] 15. Kwong, M.K. and Zettl, A., Weighted norm inequalities of sum form involving derivatives, Proc. Roy. Soc. Edinburgh A88(1981), 121-134. Google Scholar

[16] 16. Lin, C.S., Interpolation inequalities with weights, Comm. Partial Differential Eqs. 11(1986), 1515–1538. Google Scholar

[17] 17. Opic, B., Necessary and sufficient conditions for imbedding in weighted Sobolev spaces, Càsopis pro pěst Math. 114(1989), 165–175. Google Scholar

[18] 18. Triebel, H., “Interpolation Theory, Function Spaces, Differential Operators,” North Holland, Amsterdam, 1978. Google Scholar

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