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Brownian Sheet Images and Bessel-Riesz Capacity

Davar Khoshnevisan
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Abstract

We show that the image of a 2-dimensional set under d-dimensional, 2-parameter Brownian sheet can have positive Lebesgue measure, if and only if the set in question has positive (d/2)-dimensional Bessel-Riesz capacity. Our methods solve a problem of J.-P. Kahane.

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Davar Khoshnevisan. 1998-04-10. Brownian Sheet Images and Bessel-Riesz Capacity. https://arxiv.org/abs/math/9804061

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