## A convolution inequality concerning Cantor-Lebesgue measures.(English)Zbl 0644.42011

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

### MSC:

 42A85 Convolution, factorization for one variable harmonic analysis 28A25 Integration with respect to measures and other set functions
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