Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
function spaces embedding theorems; embedding theorems
function spaces embedding theorems; embedding theorems
Summary:
The paper deals with embeddings of function spaces of variable order of differentiation in function spaces of variable order of integration. Here the function spaces of variable order of differentiation are defined by means of pseudodifferential operators.
References:
[ER] Edmunds, D. E. and Rákosník, J.: Density of smooth functions in $W^{k,p(x)}$. Proc. R. Soc. Lond. A 437 (1992), 229–236. DOI 10.1098/rspa.1992.0059 | MR 1177754
[Il] Illner R.: A class of $L^p$-bounded pseudodifferential operators. Proc. Amer. Mat. Soc. 51 (1975), 347–355. MR 0383153 | Zbl 0279.47017
[JL] Jacob, N. and Leopold, H.-G.: Pseudodifferential operators with variable order of differentiation generating Feller semigroups. Integral Equations and Operator Theory 17 (1994), 151–166. MR 1243995
[KN] Kikuchi, K. and Negoro, A.: Pseudodifferential operators and Sobolev spaces of variable order of differentiation. Rep. Fac. Liberal Arts, Shizuoka University, Sciences, 31 (1995), 19–27.
[KR] Kováčik, O. and Rákosník, J.: On spaces $L^{p(x)}$ and $W^{k,p(x)}$. Czechoslovak Math. J. 41 (1991), 592–618. MR 1134951
[Kg] Kumano-go, H.: Pseudo-Differential Operators. Massachusetts Institute of Technology Press, Cambridge (Massachusetts)-London, 1981.
[Le1] Leopold, H.-G.: On Besov spaces of variable order of differentiation. Z. Anal. Anw. 8 (1989), 69–82. DOI 10.4171/ZAA/337 | MR 0997292 | Zbl 0687.46019
[Le2] Leopold, H.-G.: On function spaces of variable order of differentiation. Forum Math. 3 (1991), 1–21. DOI 10.1515/form.1991.3.1 | MR 1085592 | Zbl 0737.46020
[Ne] Negoro, A.: Stable-like processes; construction of the transition density and the behavior of sample paths near $t=0$. Osaka J. Math. 31 (1994), 189–214. MR 1262797 | Zbl 0804.60074
[Sa] Samko, S. G.: Differentiation and integration of variable order and the spaces $L^{p(x)}$. Preprint, 1996. MR 1486602
[Sh] Sharapudinov, I. I.: On a topology of the space $L^{p(t)}([0,1])$. Matem. Zametki 26 (1979), 613–632. MR 0552723
[Ta] Taylor, M. E.: Pseudodifferential Operators. Princeton University Press, Princeton (New Jersey), 1981. MR 0618463 | Zbl 0453.47026
[Tr] Triebel, H.: Theory of Function Spaces. Birkhäuser, Basel, 1983. MR 0781540 | Zbl 0546.46028
[Ts] Tsenov, I. V.: A generalization of the problem of the best approximation in the space $L^s$. Uchen. Zap. Daghestan Gos. Univ 7 (1961), 25–37.
Search
Partner of
