Kitada, Toshiyuki Multipliers on weighted Hardy spaces over certain totally disconnected groups. (English) Zbl 0662.43004 Int. J. Math. Math. Sci. 11, No. 4, 665-674 (1988). Let G be a totally disconnected, locally compact abelian group. Certain weighted function spaces over G are introduced: \(L^ 1_{\alpha}(G)\) and \(H^ 1_{\alpha}(G)\subset L^ 1_{\alpha}(G)\). Let the symbols \(\wedge\) and \(\vee\) denote Fourier and inverse Fourier transform, respectively. A function \(m\in L^{\infty}(G)\) is called an (X,Y)- multiplier if there exists a constant C such that \(\| m\phi^{\wedge})^{\vee}\|_ Y\leq C\| \phi \|_ X\), for all test functions \(\phi\). The results of this paper consist in a description of certain \((H^ 1_{\alpha},L^ 1_{\alpha})\)-multipliers as well as certain \((H^ 1_{\alpha},H^ 1_{\alpha})\)-multipliers. The details are lengthy. Reviewer: E.J.Akutowicz Cited in 4 Documents MSC: 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A70 Analysis on specific locally compact and other abelian groups 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups Keywords:totally disconnected, locally compact abelian group; weighted function spaces; inverse Fourier transform; multipliers PDFBibTeX XMLCite \textit{T. Kitada}, Int. J. Math. Math. Sci. 11, No. 4, 665--674 (1988; Zbl 0662.43004) Full Text: DOI EuDML