MATHEMATICA BOHEMICA, Vol. 129, No. 2, pp. 181-217 (2004)

Multipliers of spaces of derivatives

Jan Marik, Clifford E. Weil

Clifford E. Weil, Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, U.S.A., e-mail:

Abstract: 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.

Keywords: spaces of derivatives, Peano derivatives, Lipschitz function, multiplication operator

Classification (MSC2000): 26A21, 47B37

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