A note on function spaces in rough domains

Hans Triebel

Informatics and Automation, Function spaces, approximation theory, and related problems of mathematical analysis, Tome 293 (2016), pp. 346-351.

Résumé

This paper deals with some function spaces $B^s_{p,p}(\Omega)$ in rough domains $\Omega$ in $\mathbb R^n$.

Bibliographie

[1] Besov O.V., “Prostranstva funktsii tipa Lizorkina–Tribelya na neregulyarnoi oblasti”, Tr. MIAN, 260 (2008), 32–43 | MR | Zbl

[2] Besov O.V., “Function spaces of Lizorkin–Triebel type on an irregular domain”, Nonlinear Anal. Theory Methods. Appl. A., 70:8 (2009), 2842–2845 | DOI | MR | Zbl

[3] Besov O.V., “Prostranstva funktsii drobnoi gladkosti na neregulyarnoi oblasti”, DAN, 425:4 (2009), 439–442 | MR | Zbl

[4] Besov O.V., “Teorema vlozheniya Soboleva dlya anizotropno neregulyarnykh oblastei”, DAN, 438:5 (2011), 586–589

[5] Besov O.V., Ilin V.P., Nikolskii S.M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 ; 2-е изд., Наука, М., 1996 | MR

[6] Edmunds D.E., Triebel H., Function spaces, entropy numbers, differential operators, Cambridge Univ. Press, Cambridge, 1996 | MR | Zbl

[7] Ihnatsyeva L., Vähäkangas A.V., “Characterization of traces of smooth functions on Ahlfors regular sets”, J. Funct. Anal., 265:9 (2013), 1870–1915 | DOI | MR | Zbl

[8] Ihnatsyeva L., Vähäkangas A., “Hardy inequalities in Triebel–Lizorkin spaces”, Indiana Univ. Math. J., 62:6 (2013), 1785–1807 | DOI | MR | Zbl

[9] Ihnatsyeva L., Vähäkangas A.V., “Hardy inequalities in Triebel–Lizorkin spaces. II: Aikawa dimension”, Ann. Mat. Pura Appl. Ser. 4, 194:2 (2015), 479–493 | DOI | MR | Zbl

[10] Maz'ya V., Sobolev spaces, 2nd ed., Springer, Berlin, 1985 | MR | Zbl

[11] Nikolskii S.M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969 ; 2-е изд., Наука, М., 1977 | MR

[12] Scharf B., “Wavelet decomposition techniques and Hardy inequalities for function spaces on cubes”, J. Approx. Theory., 178 (2014), 41–63 | DOI | MR | Zbl

[13] Sobolev S.L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Izd-vo LGU, L., 1950

[14] Triebel H., Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam, 1978 ; 2nd ed., Barth, Heidelberg, 1995 | MR | Zbl | Zbl

[15] Triebel H., Theory of function spaces, Birkhäuser, Basel, 1983 | MR | Zbl

[16] Triebel H., “Hardy inequalities in function spaces”, Math. Bohem., 124 (1999), 123–130 | MR | Zbl

[17] Triebel H., The structure of functions, Birkhäuser, Basel, 2001 | MR | Zbl

[18] Triebel H., “Non-smooth atoms and pointwise multipliers in function spaces”, Ann. Mat. Pura Appl. Ser. 4, 182:4 (2003), 457–486 | DOI | MR | Zbl

[19] Triebel H., Theory of function spaces. III, Birkhäuser, Basel, 2006 | MR | Zbl

[20] Triebel H., Function spaces and wavelets on domains, European Math. Soc., Zürich, 2008 | MR | Zbl

[21] Triebel H., Winkelvoß H., “Intrinsic atomic characterizations of function spaces on domains”, Math. Z., 221:4 (1996), 647–673 | DOI | MR | Zbl

[22] Zhou Y., “Fractional Sobolev extension and imbedding”, Trans. Amer. Math. Soc., 367:2 (2015), 959–979 | DOI | MR | Zbl