T. Hytönen

activity

20072026

most citedNon-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals

110 citations · 529 across the 44 of their papers we have counts for

collaborators

53 papers

math.FA2026

Local Matrix Muckenhoupt Weights and Quantitative Weighted Inequalities Achieving Global Best Known Exponents

Tuomas Hytönen, Dachun Yang, Wen Yuan +1

In this article, we give various real-variable properties of local Muckenhoupt matrix weights $W$ and establish the quantitative boundedness of several operators on local matrix-we…

math.FA2026

Weak-type characterizations of Sobolev and bounded variation spaces on metric measure spaces

Tuomas P. Hytönen, Dachun Yang, Wen Yuan +1

Given a complete doubling metric measure space $(X, ρ, μ)$ supporting a Poincaré inequality, we prove weak-type characterizations of the Sobolev space $W ˙^{1, p} (μ)$ and the spac…

math.CA2023

On the sense of convergence in the dyadic representation theorem

Tuomas Hytönen

The dyadic representation of any singular integral operator, as an average of dyadic model operators, has found many applications. While for many purposes it is enough to have such…

math.FA2023

Matrix-Weighted Besov-Type and Triebel--Lizorkin-Type Spaces II: Sharp Boundedness of Almost Diagonal Operators

Fan Bu, Tuomas Hytönen, Dachun Yang +1

This article is the second one of three successive articles of the authors on the matrix-weighted Besov-type and Triebel--Lizorkin-type spaces. In this article, we obtain the sharp…

math.FA2023

New Characterizations and Properties of Matrix $A_{\infty}$ Weights

Fan Bu, Tuomas Hytönen, Dachun Yang +1

We provide several new characterizations of $A_{p, \infty}$ -matrix weights, originally introduced by A. Volberg as matrix-valued substitutes of the classical $A_{\infty}$ weights. In…

math.FA2023

Some remarks on convex body domination

Tuomas P. Hytönen

Convex body domination is an important elaboration of the technique of sparse domination that has seen significant development and applications over the past ten years. In this pap…

math.FA2022★ 1 cited

Quantitative estimates for bounded holomorphic semigroups

Tuomas Hytönen, Stefanos Lappas

In this paper we revisit the theory of one-parameter semigroups of linear operators on Banach spaces in order to prove quantitative bounds for bounded holomorphic semigroups. Subse…

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

Causal sparse domination of Beurling maximal regularity operators

Tuomas Hytönen, Andreas Rosén

We prove boundedness of Calderón-Zygmund operators acting in Banach functions spaces on domains, defined by the $L_{1}$ Carleson functional and $L_{q}$ ( $1 < q < \infty$ ) Whitney averages.…

math.FA2020★ 17 cited

Extrapolation of compactness on weighted spaces: Bilinear operators

Tuomas Hytönen, Stefanos Lappas

In a previous paper, we obtained several "compact versions" of Rubio de Francia's weighted extrapolation theorem, which allowed us to extrapolate the compactness of linear operator…

math.FA2020★ 8 cited

Extrapolation of compactness on weighted spaces II: Off-diagonal and limited range estimates

Tuomas Hytönen, Stefanos Lappas

In a previous paper by one of us, a "compact version" of Rubio de Francia's weighted extrapolation theorem was proved, which allows one to extrapolate the compactness of an operato…

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.CA2020★ 4 cited

Dyadic representation theorem using smooth wavelets with compact support

Tuomas Hytönen, Stefanos Lappas

The representation of a general Calderón--Zygmund operator in terms of dyadic Haar shift operators first appeared as a tool to prove the $A_{2}$ theorem, and it has found a number of…

math.FA2020★ 15 cited

Extrapolation of compactness on weighted spaces

Tuomas Hytönen, Stefanos Lappas

Let $T$ be a linear operator that, for some $p_{1} \in (1, \infty)$ , is bounded on $L^{p_{1}} (w ~)$ for all $w ~ \in A_{p_{1}} (R^{d})$ and in addition compact on $L^{p_1}(w_1…

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…

math.CA2018★ 22 cited

The L^p-to-L^q boundedness of commutators with applications to the Jacobian operator

Tuomas P. Hytönen

Supplying the missing necessary conditions, we complete the characterisation of the $L^{p} \to L^{q}$ boundedness of commutators $[b, T]$ of pointwise multiplication and Calderón-Zygmund…

math.CA2017★ 5 cited

Multi-parameter estimates via operator-valued shifts

Tuomas Hytönen, Henri Martikainen, Emil Vuorinen

We prove new results for multi-parameter singular integrals. For example, we prove that bi-parameter singular integrals in $R^{n + m}$ satisfying natural $T 1$ type condition…

math.FA2017★ 46 cited

The space $J N_{p}$ : nontriviality and duality

Galia Dafni, Tuomas Hytönen, Riikka Korte +1

We study a function space $J N_{p}$ based on a condition introduced by John and Nirenberg as a variant of BMO. It is known that $L^{p} \subset J N_{p} ⊊ L^{p, \infty}$ , but otherwi…

math.CA2017★ 15 cited

The sharp square function estimate with matrix weight

Tuomas Hytönen, Stefanie Petermichl, Alexander Volberg

We prove the matrix $A_{2}$ conjecture for the dyadic square function, that is, a norm estimate of the matrix weighted square function, where the focus is on the sharp linear depende…

math.FA2016★ 1 cited

Dyadic representation and boundedness of non-homogeneous Calderón--Zygmund operators with mild kernel regularity

Ana Grau de la Herrán, Tuomas Hytönen

We prove a new dyadic representation theorem with applications to the $T (1)$ and $A_{2}$ theorems. In particular, we obtain the non-homogeneous $T (1)$ theorem under weaker kernel reg…

math.FA2016

Vector-valued local approximation spaces

Tuomas Hytönen, Jori Merikoski

We prove that for every Banach space $Y$ , the Besov spaces of functions from the $n$ -dimensional Euclidean space to $Y$ agree with suitable local approximation spaces with equivale…

math.FA2016

Heat flow and quantitative differentiation

Tuomas Hytönen, Assaf Naor

For every Banach space $(Y, ∥ \cdot ∥_{Y})$ that admits an equivalent uniformly convex norm we prove that there exists $c = c (Y) \in (0, \infty)$ with the following property. Suppose that…

math.CA2016★ 2 cited

A Two-weight inequality between $L^{p} (ℓ^{2})$ and $L^{p}$

Tuomas Hytönen, Emil Vuorinen

We consider boundedness of a certain positive dyadic operator $T^{σ} : L^{p} (σ; ℓ^{2}) \to L^{p} (ω),$ that arose during our attempts to develop a two-weight theory for the…

math.CA2015

Quantitative weighted estimates for rough homogeneous singular integrals

Tuomas P. Hytönen, L. Roncal, Olli Tapiola

We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weig…

Local Matrix Muckenhoupt Weights and Quantitative Weighted Inequalities Achieving Global Best Known Exponents

Weak-type characterizations of Sobolev and bounded variation spaces on metric measure spaces

On the sense of convergence in the dyadic representation theorem

Matrix-Weighted Besov-Type and Triebel--Lizorkin-Type Spaces II: Sharp Boundedness of Almost Diagonal Operators

New Characterizations and Properties of Matrix A∞​ Weights

Some remarks on convex body domination

Quantitative estimates for bounded holomorphic semigroups

Fractional Bloom boundedness and compactness of commutators

Causal sparse domination of Beurling maximal regularity operators

Extrapolation of compactness on weighted spaces: Bilinear operators

Extrapolation of compactness on weighted spaces II: Off-diagonal and limited range estimates

Off-diagonal estimates for bi-commutators

Dyadic representation theorem using smooth wavelets with compact support

Extrapolation of compactness on weighted spaces

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

The L^p-to-L^q boundedness of commutators with applications to the Jacobian operator

Multi-parameter estimates via operator-valued shifts

The space JNp​: nontriviality and duality

The sharp square function estimate with matrix weight

Dyadic representation and boundedness of non-homogeneous Calderón--Zygmund operators with mild kernel regularity

Vector-valued local approximation spaces

Heat flow and quantitative differentiation

A Two-weight inequality between Lp(ℓ2) and Lp

Quantitative weighted estimates for rough homogeneous singular integrals

New Characterizations and Properties of Matrix $A_{\infty}$ Weights

The space $J N_{p}$ : nontriviality and duality

A Two-weight inequality between $L^{p} (ℓ^{2})$ and $L^{p}$