Christ, Michael A convolution inequality concerning Cantor-Lebesgue measures. (English) Zbl 0644.42011 Rev. Mat. Iberoam. 1, No. 4, 79-83 (1985). Denoting with \(\mu_{\lambda}\) the totally singular probability measure associated to the Cantor set \(E_{\lambda}\) of constant ratio of dissection \(\lambda\) on the circle group, the author proves that for any \(p\in (1,\infty)\) and for any real \(\lambda >2\), there exists \(q(p,\lambda)>p\) such that \(\| f^*\mu_{\lambda}\|_ q\leq \| f\|_ q\) for all \(f\in L^ p\). In this way the results of D. L. Ritter and W. Beckner, S. Janson, and D. Jerison are extended. Reviewer: L.Goras Cited in 10 Documents MSC: 42A85 Convolution, factorization for one variable harmonic analysis 28A25 Integration with respect to measures and other set functions Keywords:Cantor-Lebesgue measures; convolution; totally singular probability measure PDFBibTeX XMLCite \textit{M. Christ}, Rev. Mat. Iberoam. 1, No. 4, 79--83 (1985; Zbl 0644.42011) Full Text: DOI EuDML