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Evgueni Doubtsov

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Preprint Sep 2026

Sharp weighted $L^1$ bounds for Coulomb fields on the sphere

Let $d \ge 2$, let $\alpha_1,\dots, \alpha_n>0$, and put $A = \sum_k \alpha_k$. We determine, up to constants depending only on $d$, the smallest possible $L^1$ norm in the unit ball $\mathbb{B}^d\subset \mathbb{R}^d$ of the Coulomb field generated by charges of strengths $\alpha_k$ placed on the unit sphere $\mathbb{S...

Evgueni Doubtsov, I. Vasilyev, Grigory Voinov · 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

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