Author

E. Abakumov

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Preprint Sep 2026

Invariant sets of the double Hilbert transform

We present an example that shows that the double Hilbert transform $\H$ can have the characteristic function of an open set of finite measure in $\mathbb{R} \times \mathbb{R}$ as an approximate eigenvector for the eigenvalue $1$. The same holds for the dyadic model of $\H$, the double dyadic shift. We further construct...

E. Abakumov, K. Domelevo, S. Petermichl et al. · 0 citations

Preprint Jul 2026

Square function characterization of Hardy-type spaces

The well-known characterization of Hardy spaces $\mathrm{H}_{p}(\mathbb D)$, $0<p<\infty$, in terms of the Littlewood-Paley g-function $$ S f (\zeta) = \left(\int_0^1 |f'(r \zeta)|^2 (1 - r) \mathrm dr\right)^{1/2} \in \mathrm{L}_{p} $$ is generalized to Hardy-type spaces $X_A$ corresponding to quasi-Banach lattices $X...

E. Abakumov, Evgueni Doubtsov, D. Rutsky · 0 citations