| Title:
|
Embedding of function spaces of variable order of differentiation in function spaces of variable order of integration (English) |
| Author:
|
Leopold, Hans-Gerd |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
633-644 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
function spaces embedding theorems |
| Keyword:
|
embedding theorems |
| MSC:
|
35S05 |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 1008.46015 |
| idMR:
|
MR1708338 |
| . |
| Date available:
|
2009-09-24T10:26:01Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127515 |
| . |
| Reference:
|
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| Reference:
|
[Il] Illner R.: A class of $L^p$-bounded pseudodifferential operators.Proc. Amer. Mat. Soc. 51 (1975), 347–355. Zbl 0279.47017, MR 0383153 |
| Reference:
|
[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 |
| Reference:
|
[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. |
| Reference:
|
[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 |
| Reference:
|
[Kg] Kumano-go, H.: Pseudo-Differential Operators.Massachusetts Institute of Technology Press, Cambridge (Massachusetts)-London, 1981. |
| Reference:
|
[Le1] Leopold, H.-G.: On Besov spaces of variable order of differentiation.Z. Anal. Anw. 8 (1989), 69–82. Zbl 0687.46019, MR 0997292, 10.4171/ZAA/337 |
| Reference:
|
[Le2] Leopold, H.-G.: On function spaces of variable order of differentiation.Forum Math. 3 (1991), 1–21. Zbl 0737.46020, MR 1085592, 10.1515/form.1991.3.1 |
| Reference:
|
[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. Zbl 0804.60074, MR 1262797 |
| Reference:
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[Sa] Samko, S. G.: Differentiation and integration of variable order and the spaces $L^{p(x)}$.Preprint, 1996. MR 1486602 |
| Reference:
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[Sh] Sharapudinov, I. I.: On a topology of the space $L^{p(t)}([0,1])$.Matem. Zametki 26 (1979), 613–632. MR 0552723 |
| Reference:
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[Ta] Taylor, M. E.: Pseudodifferential Operators.Princeton University Press, Princeton (New Jersey), 1981. Zbl 0453.47026, MR 0618463 |
| Reference:
|
[Tr] Triebel, H.: Theory of Function Spaces.Birkhäuser, Basel, 1983. Zbl 0546.46028, MR 0781540 |
| Reference:
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[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. |
| . |
