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math.CA2025
Marstrand's density theorem for arbitrary norms in the plane
Giacomo Del Nin, Andrea Merlo
We show that if a non-trivial measure in the plane admits, at almost every point, positive and finite -dimensional density with respect to some norm, then must be an integer…
math.CA2021
Endpoint Fourier restriction and unrectifiability
Giacomo Del Nin, Andrea Merlo
We show that if a measure of dimension on admits Fourier restriction for some endpoint exponents allowed by its dimension, namely for…
math.CA2020
Rectifiability of the jump set of locally integrable functions
Giacomo Del Nin
In this note we show that for every measurable function on the set of points where the blowup exists and is not constant is -rectifiable. In particular, for e…