# Article

 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 .

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