arXiv subjects

Aapo Laukkarinen

Publications and source records attributed to Aapo Laukkarinen.

5 recordsLinked to original sources

arXiv2026

Sparse domination implies convex body domination

We prove that sparse domination of a bilinear form implies convex body domination. More precisely, if a bilinear form admits an $(r,s)$-sparse bound, then its coordinate-wise extension to $\mathbb C^n$-valued functions admits an $(r,s)$-convex body sparse bound. The proof relies on a randomization argument. We establish the result both for sparse families in a fixed dyadic lattice and for sparse families of arbitrary cubes. As an application, we deduce sparse domination for iterated commutators, with the local oscillations of the symbol appearing in the sparse form.

math.CA↗

arXiv2026

On off-diagonal operators in matrix-weighted spaces

In this paper we prove matrix-weighted inequalities for fractional operators and their commutators. We do so by developing the theory of convex body domination for such operators. Using this approach we prove quantitative estimates for the fractional integral operator (or Riesz potential) and its commutators, and prove matrix-weighted Gagliardo-Nirenberg-Sobolev inequalities for vector-valued functions.

math.CA↗

arXiv2025

Compactness of commutators of rough singular integrals

We study the two-weighted off-diagonal compactness of commutators of rough singular integral operators $T_Ω$ that are associated with a kernel $Ω\in L^q(\mathbb{S}^{d-1})$. We establish a characterisation of compactness of the commutator $[b,T_Ω]$ in terms of the function $b$ belonging to a suitable space of functions with vanishing mean oscillation. Our results expand upon the previous compactness characterisations for Calderón-Zygmund operators. Additionally, we prove a matrix-weighted compactness result for $[b,T_Ω]$ by applying the so-called matrix-weighted Kolmogorov-Riesz theorem.

math.CA↗

arXiv2024

Convex body domination for rough singular integrals

Convex body domination is a technique, where operators acting on vector-valued functions are estimated via certain convex body averages of the input functions. This domination lets one deduce various matrix weighted bounds for these operators and their commutators. In this paper, we extend the sparse domination results for rough singular integrals due to Conde-Alonso, Culiuc, Di Plinio and Ou to the convex body setting. In particular, our methods apply to homogeneous rough singular integrals with unbounded angular part. We also note that convex body domination implies new two weight commutator bounds even in the scalar case.

math.CA↗

arXiv2023

Convex body domination for a class of multi-scale operators

The technique of sparse domination, i.e., dominating operators with sums of averages taken over sparsely distributed cubes, has seen rapid development recently within the realms of harmonic analysis. A useful extension of sparse domination called convex body domination allows one to estimate operators in matrix-weighted spaces. In this paper, we extend recent sparse domination results for a class of multi-scale operators due to Beltran, Roos and Seeger to the convex body setting and prove that this implies quantitative matrix-weighted norm bounds for these operators and their commutators.

math.FA↗