Convolution estimates for some measures on curves. (English) Zbl 0613.43002

The author conjectures that if \(\lambda\) is a nice measure supported on a nice k-dimensional surface in \({\mathbb{R}}^ n\), then \(\lambda *L^ p\subset L^ q\) precisely when (1/p,1/q) is in the closed triangle in \({\mathbb{R}}^ 2\) with vertices (0,0), (1,1) and (n/(2n-k), (n-k)/(2n-k)). The paper gives partial results about this conjecture.
Reviewer: K.Saka


43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.
43A05 Measures on groups and semigroups, etc.
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