Tuomas Oikari

activity

20192026

most citedFractional Bloom boundedness and compactness of commutators

8 citations · 20 across the 15 of their papers we have counts for

collaborators

16 papers

math.CA2026

Bounds for the maximal and Riesz potential operators with variable fractionality

Francisco Gonçalves, Tuomas Oikari

We prove $L^{p (\cdot)}$ -to- $L^{q (\cdot)}$ bounds for variable versions of the fractional maximal $M^{α (\cdot)}$ and Riesz potential $I^{α (\cdot)}$ operators. The changing fractiona…

math.CA2025

Domains with globally exponentially integrable parabolic forward-in-time BMO

Kim Myyryläinen, Tuomas Oikari, Olli Saari

We characterize those open sets of the space time in which parabolic forward-in-time BMO functions are in a certain forward-in-time exponential integrability class. The characteriz…

math.FA2025

Factorizations for variable exponent Muckenhoupt weights

Stefanos Lappas, Tuomas Oikari

Given two variable exponent Muckenhoupt weights $w \in A_{p (\cdot)}$ and $w_{1} \in A_{p_{1} (\cdot)}$ , we prove that for all small enough $θ > 0,$ there holds that $w_0…

math.FA2024

Testing compactness of linear operators

Timo S. Hänninen, Tuomas Oikari, Tuomas V. Oikari

Let $(F_{i})$ be a sequence of sets in a Banach space $X$ . For what sequences does the condition $i \to \infty lim f_{i} \in F_{i} sup ∥ T f_{i} ∥_{Y} = 0$ hold for every Banach space $…

math.CA2024

On the compactness of the bi-commutator

Henri Martikainen, Tuomas Oikari

We prove compactness results and characterizations for the bi-commutator $[T_{1}, [b, T_{2}]]$ of a symbol $b$ and two non-degenerate Calderón-Zygmund singular integral operators $T_1,…

math.CA2024

Curved commutators in the plane

Kangwei Li, Henri Martikainen, Tuomas Oikari

We complete the $L^{p}$ boundedness theory of commutators of Hilbert transforms along monomial curves by providing the previously missing lower bounds. This optimal result now covers…

math.CA2024

Note on the compactness of commutators

Tuomas Oikari

The optimal sufficient conditions for the $L^{p}$ -to- $L^{q}$ compactness of commutators of singular integral operators of both Calderón-Zygmund and of rough type are shown in the diffe…

math.CA2024

Traces of vanishing Hölder spaces

Kaushik Mohanta, Carlos Mudarra, Tuomas Oikari

For an arbitrary subset $E \subset R^{n},$ we introduce and study the three vanishing subspaces of the Hölder space $C ˙^{0, ω} (E)$ consisting of those functions for which…

math.FA2024

Approximation in Hölder Spaces

Carlos Mudarra, Tuomas Oikari

We introduce new vanishing subspaces of the homogeneous Hölder space $C ˙^{0, ω} (X, Y)$ in the generality of a doubling modulus $ω$ and normed spaces $X$ and $Y .$ For many couple…

math.CA2023

On the $L^{p}$ -to- $L^{q}$ boundedness and compactness of commutators along monomial curves

Tuomas Oikari

For exponents $p, q \in (1, \infty),$ we study the $L^{p}$ -to- $L^{q}$ boundedness and compactness of the commutator $[b, H_{γ}] = b H_{γ} - H_{γ} b,$ where $H_{γ}$ is the Hilbert transform along the…

math.CA2022★ 8 cited

Fractional Bloom boundedness and compactness of commutators

Tuomas Hytönen, Tuomas Oikari, Jaakko Sinko

Let $T$ be a non-degenerate Calderón-Zygmund operator and let $b : R^{d} \to C$ be locally integrable. Let $1 < p \leq q < \infty$ and let $μ^{p} \in A_{p}$ and $λ^{q} \in A_{q},$ whe…

math.CA2021★ 1 cited

Lower bound of the parabolic Hilbert commutator

Tuomas Oikari

Answering a key point left open in a recent work of Bongers, Guo, Li and Wick, we provide the following lower bound $$ \|b\|_{\text{BMO}_γ(\mathbb{R}^2)}\lesssim \|[b,H_γ]\|_{L^p(\…

math.CA2021★ 1 cited

Off-diagonal estimates for bilinear commutators

Tuomas Oikari

We find a minimal notion of non-degeneracy for bilinear singular integral operators $T$ and identify testing conditions on the multiplying function $b$ that characterize the $L^p\t…

math.CA2020

Off-diagonal estimates for commutators of bi-parameter singular integrals

Tuomas Oikari

We study the boundedness of commutators of bi-parameter singular integrals between mixed spaces $[b, T] : L^{p_{1}} L^{p_{2}} \to L^{q_{1}} L^{q_{2}}$ in the off-diagonal situation $q_i,p_…

math.CA2020★ 8 cited

Off-diagonal estimates for bi-commutators

Emil Airta, Tuomas Hytönen, Kangwei Li +2

We study the bi-commutators $[T_{1}, [b, T_{2}]]$ of pointwise multiplication and Calderón-Zygmund operators, and characterize their $L^{p_{1}} L^{p_{2}} \to L^{q_{1}} L^{q_{2}}$ boundedness for…

math.CA2019★ 2 cited

Iterated commutators under a joint condition on the tuple of multiplying functions

Tuomas Hytönen, Kangwei Li, Tuomas Oikari

We present a pair of joint conditions on the two functions $b_{1}, b_{2}$ strictly weaker than $b_{1}, b_{2} \in BMO$ that almost characterize the $L^{2}$ boundedness of the iter…

Bounds for the maximal and Riesz potential operators with variable fractionality

Domains with globally exponentially integrable parabolic forward-in-time BMO

Factorizations for variable exponent Muckenhoupt weights

Testing compactness of linear operators

On the compactness of the bi-commutator

Curved commutators in the plane

Note on the compactness of commutators

Traces of vanishing Hölder spaces

Approximation in Hölder Spaces

On the Lp-to-Lq boundedness and compactness of commutators along monomial curves

Fractional Bloom boundedness and compactness of commutators

Lower bound of the parabolic Hilbert commutator

Off-diagonal estimates for bilinear commutators

Off-diagonal estimates for commutators of bi-parameter singular integrals

Off-diagonal estimates for bi-commutators

Iterated commutators under a joint condition on the tuple of multiplying functions

On the $L^{p}$ -to- $L^{q}$ boundedness and compactness of commutators along monomial curves