Aleksi Pyorala

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math.CA2025

Furstenberg set theorem for transversal families of functions

Tuomas Orponen, Aleksi PyÃ¶rÃ¤lÃ¤, Guangzeng Yi

We prove an extension of the Furstenberg set theorem to families of graphs satisfying a transversality condition. We apply the result to derive bounds on $L^{p}$ -norms of Fourier t…

math.CA2025

On Fourier transforms of fractal measures on the parabola

Tuomas Orponen, Carmelo Puliatti, Aleksi PyÃ¶rÃ¤lÃ¤

Let $s \in [0, 1]$ and $t \in [0, min {3 s, s + 1})$ . Let $I ¨ $ be a Borel measure supported on the parabola $P = {(x, x^{2}) : x \in [- 1, 1]}$ satisfying the $s$ -dimensional…