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A convolution property of some measures with self-similar fractal support

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Szecsei D.

Colloquium Mathematicum

2007

tom 109

nr 2

171-177

We define a class of measures having the following properties: (1) the measures are supported on self-similar fractal subsets of the unit cube $I^{M} = [0,1)^{M}$, with 0 and 1 identified as necessary; (2) the measures are singular with respect to normalized Lebesgue measure m on $I^{M}$; (3) the measures have the convolution property that $μ∗ L^{p} ⊆ L^{p+ε}$ for some ε = ε(p) > 0 and all p ∈ (1,∞). We will show that if (1/p,1/q) lies in the triangle with vertices (0,0), (1,1) and (1/2,1/3), then $μ ∗ L^{p} ⊆ L^{q}$ for any measure μ in our class.

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1 Colloquium Mathematicum

1 Szecsei D.

1 2007

Wyniki wyszukiwania

A convolution property of some measures with self-similar fractal support