Emil Vuorinen

activity

20142023

most citedEnd-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications

26 citations · 77 across the 18 of their papers we have counts for

collaborators

23 papers

math.CA2023

The Strong Matrix Weighted Maximal Operator

Emil Vuorinen

The purpose of this note is to prove that the strong Christ-Goldberg maximal function is bounded. This is a matrix weighted maximal operator appearing in the theory of matrix weigh…

math.CA2022

Exotic Calderón-Zygmund operators

Tuomas Hytönen, Kangwei Li, Henri Martikainen +1

We study singular integral operators with kernels that are more singular than standard Calderón-Zygmund kernels, but less singular than bi-parameter product Calderón-Zygmund kernel…

math.CA2022★ 3 cited

Multiresolution analysis and Zygmund dilations

Tuomas Hytönen, Kangwei Li, Henri Martikainen +1

Zygmund dilations are a group of dilations lying in between the standard product theory and the one-parameter setting - in $\mathbb{R}^3 = \mathbb{R} \times \mathbb{R} \times \math…

math.CA2020★ 2 cited

Genuinely multilinear weighted estimates for singular integrals in product spaces

Kangwei Li, Henri Martikainen, Emil Vuorinen

We prove genuinely multilinear weighted estimates for singular integrals in product spaces. The estimates complete the qualitative weighted theory in this setting. Such estimates w…

math.CA2020★ 3 cited

Modern singular integral theory with mild kernel regularity

Emil Airta, Henri Martikainen, Emil Vuorinen

We present a framework based on modified dyadic shifts to prove multiple results of modern singular integral theory under mild kernel regularity. Using new optimized representation…

math.CA2019

Banach-valued multilinear singular integrals with modulation invariance

Francesco Di Plinio, Kangwei Li, Henri Martikainen +1

We prove that the class of trilinear multiplier forms with singularity over a one dimensional subspace, including the bilinear Hilbert transform, admit bounded $L^{p}$ -extension to t…

math.CA2019★ 3 cited

Some new weighted estimates on product spaces

Emil Airta, Kangwei Li, Henri Martikainen +1

We complete our theory of weighted $L^{p} (w_{1}) \times L^{q} (w_{2}) \to L^{r} (w_{1}^{r / p} w_{2}^{r / q})$ estimates for bilinear bi-parameter Calderón--Zygmund operators under the assumption that…

math.CA2019★ 1 cited

Multilinear operator-valued Calderón-Zygmund theory

Francesco Di Plinio, Kangwei Li, Henri Martikainen +1

We develop a general theory of multilinear singular integrals with operator-valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multi…

math.CA2019

Multilinear singular integrals on non-commutative $L^{p}$ spaces

Francesco Di Plinio, Kangwei Li, Henri Martikainen +1

We prove $L^{p}$ bounds for the extensions of standard multilinear Calderón-Zygmund operators to tuples of UMD spaces tied by a natural product structure. This can, for instance, mea…

math.CA2019★ 26 cited

End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications

Kangwei Li, José María Martell, Henri Martikainen +2

In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the so…

math.CA2018

Bloom type upper bounds in the product BMO setting

Kangwei Li, Henri Martikainen, Emil Vuorinen

For a bounded singular integral $T_{n}$ in $R^{n}$ and a bounded singular integral $T_{m}$ in $R^{m}$ we prove that $$ \| [T_n^1, [b, T_m^2]] \|_{L^p(μ) \to L^p(λ)} \less…

math.CA2018

Quasi-Banach estimates of commutators of bilinear bi-parameter singular integrals: paraproducts

Kangwei Li, Henri Martikainen, Emil Vuorinen

We complete our boundedness theory of commutators of bilinear bi-parameter singular integrals by establishing the following result. If $T$ is a bilinear bi-parameter singular integ…

math.CA2018

Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators

Kangwei Li, Henri Martikainen, Emil Vuorinen

Utilising some recent ideas from our bilinear bi-parameter theory, we give an efficient proof of a two-weight Bloom type inequality for iterated commutators of linear bi-parameter…

math.CA2018★ 2 cited

Commutators of bilinear bi-parameter singular integrals

Kangwei Li, Henri Martikainen, Emil Vuorinen

We study the boundedness properties of commutators formed by $b$ and $T$ , where $T$ is a bilinear bi-parameter singular integral satisfying natural $T 1$ type conditions and $b$ is…

math.CA2017★ 21 cited

Bilinear Calderón-Zygmund theory on product spaces

Kangwei Li, Henri Martikainen, Emil Vuorinen

We develop a wide general theory of bilinear bi-parameter singular integrals $T$ . First, we prove a dyadic representation theorem starting from $T 1$ assumptions and apply it to sho…

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.CA2017★ 1 cited

Bilinear representation theorem

Kangwei Li, Henri Martikainen, Yumeng Ou +1

We represent a general bilinear Calderón-Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In partic…

math.CA2016

Dyadic-probabilistic methods in bilinear analysis

Henri Martikainen, Emil Vuorinen

We demonstrate and develop dyadic-probabilistic methods in connection with non-homogeneous bilinear operators, namely singular integrals and square functions. We develop the full n…

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.CA2016★ 2 cited

Non-homogeneous square functions on general sets: suppression and big pieces methods

Henri Martikainen, Mihalis Mourgoglou, Emil Vuorinen

We aim to showcase the wide applicability and power of the big pieces and suppression methods in the theory of local $T b$ theorems. The setting is new: we consider conical square f…

math.CA2015

A new approach to non-homogeneous local $T b$ theorems

Henri Martikainen, Mihalis Mourgoglou, Emil Vuorinen

We develop a new general method to prove various non-doubling local Tb theorems. The method combines the non-homogeneous good lambda method of Tolsa, the big pieces Tb theorem of N…

math.CA2015

Two weight $L^{p}$ -inequalities for dyadic shifts and the dyadic square function

Emil Vuorinen

We consider two weight $L^{p} \to L^{q}$ -inequalities for dyadic shifts and the dyadic square function with general exponents $1 < p, q < \infty$ . It is shown that if a so-called quadrat…

math.CA2014★ 6 cited

L^{p}(μ)-L^{q}(ν) characterization for well localized operators

Emil Vuorinen

We consider a two weight $L^{p} (μ) \to L^{q} (ν)$ -inequality for well localized operators as defined and studied by F. Nazarov, S. Treil and A. Volberg when $p = q = 2$ . A counterexampl…

The Strong Matrix Weighted Maximal Operator

Exotic Calderón-Zygmund operators

Multiresolution analysis and Zygmund dilations

Genuinely multilinear weighted estimates for singular integrals in product spaces

Modern singular integral theory with mild kernel regularity

Banach-valued multilinear singular integrals with modulation invariance

Some new weighted estimates on product spaces

Multilinear operator-valued Calderón-Zygmund theory

Multilinear singular integrals on non-commutative Lp spaces

End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications

Bloom type upper bounds in the product BMO setting

Quasi-Banach estimates of commutators of bilinear bi-parameter singular integrals: paraproducts

Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators

Commutators of bilinear bi-parameter singular integrals

Bilinear Calderón-Zygmund theory on product spaces

Multi-parameter estimates via operator-valued shifts

Bilinear representation theorem

Dyadic-probabilistic methods in bilinear analysis

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

Non-homogeneous square functions on general sets: suppression and big pieces methods

A new approach to non-homogeneous local Tb theorems

Two weight Lp-inequalities for dyadic shifts and the dyadic square function

L^{p}(μ)-L^{q}(ν) characterization for well localized operators

Multilinear singular integrals on non-commutative $L^{p}$ spaces

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

A new approach to non-homogeneous local $T b$ theorems

Two weight $L^{p}$ -inequalities for dyadic shifts and the dyadic square function