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Possibilities for defining the radial derivative of the delta distribution $\delta(\underline{x})$ in the setting of spherical coordinates are explored. This leads to the introduction of a new class of continuous linear functionals similar to but different from the standard distributions. The radial derivative of $\delta(\underline{x})$ then belongs to that new class of so-called signumdistributions. It is shown that these signumdistributions obey easy-to-handle calculus rules which are in accordance with those for the standard distributions in $\mathbb{R}^m$., Comment: 18 pages

In this paper, we obtain complete characterizations of the boundedness and compactness of the products of the multiplication and the radial derivative operator MuR from mixed norm spaces \({H(p, q, \phi)}\) to Zygmund-type spaces on the unit ball.