3 problems

Zygmund's conjecture. The operator $M_{\Gamma}$ is bounded on $L^p(\mathbb{R}^2)$ for every $1<p<\infty$.

Let $v$ be a two-variable vector field and define … More precisely, for $0<L<1$, the source defines $M_v$ by the centered averages … Assume that $v_\infty$ is bounded and that the…

Aversa and Preiss constructed a sequence of compact positive-measure sets whose dilates have the affine density property. Aversa–Preiss conjecture. Their construction could be stre…