@article{bwmeta1.element.bwnjournal-article-smv140i2p141bwm, author = {V. Rychkov}, title = {Linear extension operators for restrictions of function spaces to irregular open sets}, journal = {Studia Mathematica}, volume = {141}, year = {2000}, pages = {141-162}, zbl = {0972.46018}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv140i2p141bwm} }
Rychkov, V. Linear extension operators for restrictions of function spaces to irregular open sets. Studia Mathematica, Tome 141 (2000) pp. 141-162. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv140i2p141bwm/
[00000] [1] D. R. Adams, The classification problem for the capacities associated with the Besov and Triebel-Lizorkin spaces, in: Approximation and Function Spaces, Banach Center Publ. 22, PWN-Polish Sci. Publ., Warszawa, 1989, 9-24.
[00001] [2] D. R. Adams and L. I. Hedberg, Function Spaces and Potential Theory, Grundlehren Math. Wiss. 314, Springer, Berlin, 1996.
[00002] [3] Yu. A. Brudnyĭ, Spaces defined by means of local approximation, Trudy Moskov. Mat. Obshch. 24 (1971), 69-132 (in Russian).
[00003] [4] H.-Q. Bui, M. Paluszyński, and M. H. Taibleson, A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces, Studia Math. 119 (1996), 219-246. | Zbl 0861.42009
[00004] [5] P. Bylund, Besov spaces and measures on arbitrary closed sets, Univ. of Umeå, Dept. of Math., Doctoral Thesis No 8, 1994. | Zbl 0860.46021
[00005] [6] J. R. Dorronsoro, On the differentiability of Lipschitz-Besov functions, Trans. Amer. Math. Soc. 303 (1987), 229-240. | Zbl 0644.46027
[00006] [7] C. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115. | Zbl 0222.26019
[00007] [8] M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), 777-799. | Zbl 0551.46018
[00008] [9] M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), 34-170. | Zbl 0716.46031
[00009] [11] O. Frostman, Potentiel d'équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions, Medd. Lunds Univ. Mat. Sem. 3 (1935), 1-118. | Zbl 61.1262.02
[00010] [12] P. W. Jones, Quasiconformal mappings and extendability of functions in Sobolev spaces, Acta Math. 147 (1981), 71-88. | Zbl 0489.30017
[00011] [13] A. Jonsson, Besov spaces on closed sets by means of atomic decompositions, Univ. of Umeå, Dept. of Math., Research Report No 7, 1993. | Zbl 0831.46028
[00012] [14] A. Jonsson and H. Wallin, Function Spaces on Subsets of , Math. Reports 2, Part 1, Harwood, New York, 1984. | Zbl 0875.46003
[00013] [15] G. A. Kalyabin, The intrinsic norming of the retractions of Sobolev spaces onto plain domains with the points of sharpness, in: Abstracts of Conference on Functional Spaces, Approximation Theory, Nonlinear Analysis in Honor of S. M. Nikol'ski(Moscow, 1995), p. 330 (in Russian).
[00014] [16] Yu. V. Netrusov, Sets of singularities of functions in spaces of Besov and Lizorkin-Triebel type, Trudy Mat. Inst. Steklov. 187 (1989), 162-177 (in Russian); English transl.: Proc. Steklov Inst. Math. 187 (1990), 185-203.
[00015] [17] J. Peetre, On spaces of Triebel-Lizorkin type, Ark. Mat. 13 (1975), 123-130. | Zbl 0302.46021
[00016] [18] C. A. Rogers, Hausdorff Measures, Cambridge Univ. Press, Cambridge, 1970.
[00017] [19] V. S. Rychkov, On a theorem of Bui, Paluszyński, and Taibleson, Trudy Mat. Inst. Steklov. (to appear).
[00018] [20] A. Seeger, A note on Triebel-Lizorkin spaces, in: Approximation and Function Spaces, Banach Center Publ. 22, PWN-Polish Sci. Publ., Warszawa, 1989, 391-400.
[00019] [21] P. A. Shvartsman, Extension theorems with preservation of local polynomial approximations, Yaroslavl Univ., 1986; VINITI Publ. 8.08.1986, No. 6457 (in Russian).
[00020] [22] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, NJ, 1971. | Zbl 0232.42007
[00021] [23] R. Strichartz, Multipliers on fractional Sobolev spaces, J. Math. Mech. 16 (1967), 1031-1060. | Zbl 0145.38301
[00022] [24] H. Triebel, Theory of Function Spaces, Monogr. Math. 78, Birkhäuser, Basel, 1983.
[00023] [25] H. Triebel, Theory of Function Spaces II, Monogr. Math. 84, Birkhäuser, Basel, 1992.