Page 21 - Textos de Matemática Vol. 34

REMARKS ON SOBOLEV EMBEDDINGS 11
[9] D. E. Edmunds and J. Lang, Behaviour of the approximation numbers of a Sobolev embedding in the one-dimensional case, J. Funct. Anal. 206 (2004), 149-166.
[10] D. E. Edmunds and H. Triebel, Function spaces, entropy numbers, differential operators, Cambridge University Press, Cambridge, 1996.
[11] W. D. Evans, D. J. Harris and Y. Sait¯o, On the approximation numbers of Sobolev embeddings on singular domains and trees, Q. J. Math. (to appear).
[12] D. Haroske, Embeddings of some weighted function spaces on Rn; entropy and approximation numbers, An. Univ. Craiova Ser. Mat. Inform. 24 (1997), 1-44.
[13] T. Ku¨hn, H.-G. Leopold, W. Sickel and L. Skrzypczak, Entropy numbers of embeddings of weighted Besov spaces, Preprint Math/Inf/13/03, Universit¨at Jena, 2003.
[14] H.-G. Leopold, Embeddings and entropy numbers in Besov spaces of generalised smoothness, Proc. Conf. Function Spaces V, Poznan´, 1998.
[15] V. I. Levin, On a class of integral inequalities, Recueil Math´ematiques 4(46) (1938), 309-331.
[16] P. Lindqvist, Some remarkable sine and cosine functions, Ricerche Mat. 44 (1995), no. 2,
269-290.
[17] J. S. Martins, Embeddings of non-isotropic spaces, Quart. J. Math. Oxford Ser. (2) 29 (1978),
no. 114, 111-140.
[18] S. Moura, Function spaces of generalised smoothness, Dissertationes Math. 398 (2001), 88
pp.
[19] M. Oˆtani, A remark on certain nonlinear elliptic equations, Proc. Fac. Sci. Tokai Univ. 19
(1984), 23-28.
[20] E. Schmidt, U¨ber die Ungleichung, welche die Integrale u¨ber eine Potenz einer Funktion und
u¨ber eine andere Potenz ihrer Ableitung verbindet, Math. Ann. 117 (1940), 301-326.
[21] H. Triebel, Fractals and spectra, Birkh¨auser Verlag, Basel, 1997.
David E. Edmunds, Department of Mathematics, Mantell Building, University of Sussex, Brighton BN1 9RF, Sussex, UK
E-mail address: d.e.edmunds@sussex.ac.uk