| Title:
|
Multipliers of spaces of derivatives (English) |
| Author:
|
Mařík, Jan |
| Author:
|
Weil, Clifford E. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
129 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
181-217 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For subspaces, $X$ and $Y$, of the space, $D$, of all derivatives $M(X,Y)$ denotes the set of all $g\in D$ such that $fg \in Y$ for all $f \in X$. Subspaces of $D$ are defined depending on a parameter $p \in [0,\infty ]$. In Section 6, $M(X,D)$ is determined for each of these subspaces and in Section 7, $M(X,Y)$ is found for $X$ and $Y$ any of these subspaces. In Section 3, $M(X,D)$ is determined for other spaces of functions on $[0,1]$ related to continuity and higher order differentiation. (English) |
| Keyword:
|
spaces of derivatives |
| Keyword:
|
Peano derivatives |
| Keyword:
|
Lipschitz function |
| Keyword:
|
multiplication operator |
| MSC:
|
26A21 |
| MSC:
|
26A24 |
| MSC:
|
47B37 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 1051.26003 |
| idMR:
|
MR2073514 |
| DOI:
|
10.21136/MB.2004.133900 |
| . |
| Date available:
|
2009-09-24T22:14:13Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133900 |
| . |
| Reference:
|
[1] A. M. Bruckner, J. Mařík, C. E. Weil: Some aspects of products of derivatives.Amer. Math. Monthly 99 (1992), 134–145. MR 1144354, 10.2307/2324182 |
| Reference:
|
[2] R. J. Fleissner: Distant bounded variation and products of derivatives.Fundam. Math. 94 (1977), 1–11. Zbl 0347.26009, MR 0425041 |
| Reference:
|
[3] R. J. Fleissner: Multiplication and the fundamental theorem of calculus: A survey.Real Anal. Exchange 2 (1976), 7–34. MR 0507383 |
| Reference:
|
[4] J. Mařík: Multipliers of summable derivatives.Real Anal. Exchange 8 (1982–83), 486–493. MR 0700199, 10.2307/44153420 |
| Reference:
|
[5] J. Mařík: Transformation and multiplication of derivatives.Classical Real Analysis, Proc. Spec. Sess. AMS, 1982, AMS, Contemporary Mathematics 42, 1985, pp. 119–134. MR 0807985 |
| Reference:
|
[6] J. Mařík, C. E. Weil: Sums of powers of derivatives.Proc. Amer. Math. Soc. 112, 807–817. MR 1042268 |
| Reference:
|
[7] W. Wilkocz: Some properties of derivative functions.Fund. Math. 2 (1921), 145–154. 10.4064/fm-2-1-145-154 |
| Reference:
|
[8] S. Saks: Theory of the integral.Dover Publications, 1964. MR 0167578 |
| . |
