@article{RM_2005_60_6_a11,
author = {H. Triebel},
title = {Spaces on sets},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {1195--1215},
year = {2005},
volume = {60},
number = {6},
language = {en},
url = {http://geodesic.mathdoc.fr/item/RM_2005_60_6_a11/}
}
H. Triebel. Spaces on sets. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 60 (2005) no. 6, pp. 1195-1215. http://geodesic.mathdoc.fr/item/RM_2005_60_6_a11/
[1] D. R. Adams, L. I. Hedberg, Function Spaces and Potential Theory, Springer-Verlag, Berlin, 1996 | MR
[2] P. Assouad, “Plongements lipschitziens dans ${\mathbb R}^n$”, Bull. Soc. Math. France, 111:4 (1983), 429–448 | MR | Zbl
[3] O. V. Besov, V. P. Ilin, S. M. Nikolskii, Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | MR | Zbl
[4] M. Bricchi, “Complements and results on $h$-sets”, Function Spaces, Differential Operators and Nonlinear Analysis, Birkhäuser, Basel, 2003, 219–229 | MR | Zbl
[5] M. Bricchi, “Tailored Besov spaces and $h$-sets”, Math. Nachr., 263/264 (2004), 36–52 | DOI | MR | Zbl
[6] P. Bylund, Besov spaces and measures on arbitrary sets, Ph.D Thesis, University of Umeå, Umeå, 1994 | MR
[7] M. Christ, A. Seeger, Necessary conditions for vector-valued operator inequalities in harmonic analysis, arXiv: math/0504030 | MR
[8] R. A. DeVore, G. G. Lorentz, Constructive Approximation, Springer-Verlag, Berlin, 1993 | MR
[9] R. A. DeVore, R. C. Sharpley, “Besov spaces on domains in ${\mathbb R}^d$”, Trans. Amer. Math. Soc., 335:2 (1993), 843–864 | DOI | MR | Zbl
[10] D. E. Edmunds, H. Triebel, Function Spaces, Entropy Numbers, Differential Operators, Cambridge Univ. Press, Cambridge, 1996 | MR
[11] C. Fefferman, E. M. Stein, “Some maximal inequalities”, Amer. J. Math., 93 (1971), 107–115 | DOI | MR | Zbl
[12] M. Frazier, B. Jawerth, “A discrete transform and decompositions of distribution spaces”, J. Funct. Anal., 93:1 (1990), 34–170 | DOI | MR | Zbl
[13] M. Frazier, B. Jawerth, G. Weiss, Littlewood–Paley Theory and the Study of Function Spaces, Amer. Math. Soc., Providence, RI, 1991 | MR | Zbl
[14] P. Hajłasz, P. Koskela, “Sobolev met Poincaré”, Mem. Amer. Math. Soc., 145:688 (2000), 1–101 | MR
[15] Y. S. Han, E. T. Sawyer, “Littlewood–Paley theory on spaces of homogeneous type and classical function spaces”, Mem. Amer. Math. Soc., 110:530 (1994) | MR
[16] Y. Han, D. Yang, “New characterizations and applications of inhomogeneous Besov and Triebel–Lizorkin spaces on homogeneous type spaces and fractals”, Dissertationes Math. (Rozprawy Mat.), 403 (2002) | MR | Zbl
[17] Y. Han, D. Yang, “Triebel–Lizorkin spaces with non-doubling measures”, Studia Math., 162:2 (2004), 105–140 | DOI | MR | Zbl
[18] L. I. Hedberg, Yu. Netrusov, An axiomatic approach to function spaces, spectral synthesis, and Luzin approximation, Mem. Amer. Math. Soc., 882, Amer. Math. Soc., Providence, RI, 2007 | MR
[19] J. Heinonen, Lectures on Analysis on Metric Spaces, Springer-Verlag, New York, 2001 | MR | Zbl
[20] A. Jonsson, “Besov spaces on closed subsets of $\mathbb R^n$”, Trans. Amer. Math. Soc., 341:1 (1994), 355–370 | DOI | MR | Zbl
[21] P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge Univ. Press, Cambridge, 1995 | MR
[22] Yu. Netrusov, “Mnozhestva osobennostei funktsii iz prostranstv tipa Besova i Lizorkina–Tribelya”, Tr. MIAN, 187, 1989, 162–177 | MR
[23] S. M. Nikolskii, Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969 | MR
[24] S. L. Sobolev, Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Izd-vo Leningr. un-ta, L., 1950 | MR
[25] E. A. Storozhenko, P. Osvald, “Teorema Dzheksona v prostranstvakh $L^p(R^k)$, $0
1$”, Sib. matem. zhurn., 19:4 (1978), 888–901 | MR | Zbl[26] A. Torchinsky, Real-variable Methods in Harmonic Analysis, Academic Press, Orlando, FL, 1986 | MR | Zbl
[27] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, 1983 ; Kh. Tribel, Teoriya funktsionalnykh prostranstv, Mir, M., 1986 | MR | Zbl | MR | Zbl
[28] H. Triebel, Theory of Function Spaces. II, Birkhäuser, Basel, 1992 | MR | Zbl
[29] H. Triebel, Fractals and Spectra. Related to Fourier Analysis and Function Spaces, Birkhäuser, Basel, 1997 | MR | Zbl
[30] H. Triebel, The Structure of Functions, Birkhäuser, Basel, 2001 | MR | Zbl
[31] H. Triebel, “Wavelet frames for distributions; local and pointwise regularity”, Studia Math., 154:1 (2003), 59–88 | DOI | MR | Zbl
[32] H. Triebel, “Fractal characteristics of measures: An approach via function spaces”, J. Fourier Anal. Appl., 9:4 (2003), 411–430 | DOI | MR | Zbl
[33] H. Triebel, “The positivity property of function spaces”, Proceedings of the Sixth Conference “Function Spaces” (Wroclaw, 2001), ed. R. Grzaslewicz et al., World Scientific, River Edge, NJ, 2003, 263–274 | MR | Zbl
[34] H. Triebel, “A new approach to function spaces on quasi-metric spaces”, Rev. Mat. Complut., 18:1 (2005), 7–48 | MR | Zbl
[35] H. Triebel, Theory of Function Spaces. III, Birkhäuser, Basel (to appear) | MR
[36] A. L. Volberg, S. V. Konyagin, “O merakh s usloviem udvoeniya”, Izv. AN SSSR. Ser. matem., 51:3 (1987), 666–675 | MR | Zbl
[37] P. Wojtaszczyk, A Mathematical Introduction to Wavelets, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl