110 citations · 529 across the 44 of their papers we have counts for
30 papers · 1 filter
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…
Fractional Bloom boundedness and compactness of commutators
Tuomas Hytönen, Tuomas Oikari, Jaakko Sinko
Let be a non-degenerate Calderón-Zygmund operator and let be locally integrable. Let and let and whe…
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 Carleson functional and () Whitney averages.…
Off-diagonal estimates for bi-commutators
Emil Airta, Tuomas Hytönen, Kangwei Li +2
We study the bi-commutators of pointwise multiplication and Calderón-Zygmund operators, and characterize their boundedness for…
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 theorem, and it has found a number of…
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 strictly weaker than that almost characterize the boundedness of the iter…
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 boundedness of commutators of pointwise multiplication and Calderón-Zygmund…
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 satisfying natural type condition…
The sharp square function estimate with matrix weight
Tuomas Hytönen, Stefanie Petermichl, Alexander Volberg
We prove the matrix 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…
A Two-weight inequality between and
Tuomas Hytönen, Emil Vuorinen
We consider boundedness of a certain positive dyadic operator that arose during our attempts to develop a two-weight theory for the…
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…
Weak and strong - estimates for square functions and related operators
Tuomas P. Hytönen, Kangwei Li
We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main ne…
Two-weight - bounds for positive dyadic operators: unified approach to and
Timo S. Hänninen, Tuomas P. Hytönen, Kangwei Li
We characterize the boundedness of positive dyadic operators of the form and the $L^{p_1}(σ_1)…
Operator-valued dyadic shifts and the T(1) theorem
Timo S. Hänninen, Tuomas P. Hytönen
In this paper we extend dyadic shifts and the dyadic representation theorem to an operator-valued setting: We first define operator-valued dyadic shifts and prove that they are bou…
Weak A_\infty weights and weak Reverse Hölder property in a space of homogeneous type
Theresa C. Anderson, Tuomas Hytönen, Olli Tapiola
In the Euclidean setting, the Fujii-Wilson-type weights satisfy a Reverse Hölder Inequality (RHI) but in spaces of homogeneous type the best known result has been that $…
Bounds for partial derivatives: necessity of UMD and sharp constants
Alejandro J. Castro, Tuomas P. Hytönen
We prove the necessity of the UMD condition, with a quantitative estimate of the UMD constant, for any inequality in a family of bounds between different partial derivatives…
Bounded variation approximation of L_p dyadic martingales and solutions to elliptic equations
Tuomas Hytönen, Andreas Rosén
We prove continuity and surjectivity of the trace map onto , from a space of functions of locally bounded variation, defined by the Carleson functional. The extension map is c…
Non-homogeneous T1 theorem for bi-parameter singular integrals
Tuomas Hytönen, Henri Martikainen
We prove a non-homogeneous T1 theorem for certain bi-parameter singular integral operators. Moreover, we discuss the related non-homogeneous Journe's lemma and product BMO theory.
A variation norm Carleson theorem for vector-valued Walsh-Fourier series
Tuomas P. Hytönen, Michael T. Lacey, Ioannis Parissis
We prove a variation norm Carleson theorem for Walsh-Fourier series of functions with values in a UMD Banach space. Our only hypothesis on the Banach space is that it has finite ti…
The local Tb theorem with rough test functions
Tuomas Hytönen, Fedor Nazarov
We prove a local theorem under close to minimal (up to certain `buffering') integrability assumptions, conjectured by S. Hofmann (El Escorial, 2008): Every cube is assumed to…
The Vector Valued Quartile Operator
Tuomas P. Hytönen, Michael T. Lacey, Ioannis Parissis
Certain vector-valued inequalities are shown to hold for a Walsh analog of the bilinear Hilbert transform. These extensions are phrased in terms of a recent notion of quartile type…
Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals
Tuomas P. Hytönen, Michael T. Lacey, Carlos Pérez
Any Calderon-Zygmund operator T is pointwise dominated by a convergent sum of positive dyadic operators. We give an elementary self-contained proof of this fact, which is simpler t…
Pointwise convergence of Walsh--Fourier series of vector-valued functions
Tuomas P. Hytönen, Michael T. Lacey
We prove a version of Carleson's Theorem in the Walsh model for vector-valued functions: For , and a UMD space , the Walsh-Fourier series of c…
Orthonormal bases of regular wavelets in spaces of homogeneous type
Pascal Auscher, Tuomas Hytönen
Adapting the recently developed randomized dyadic structures, we introduce the notion of spline function in geometrically doubling quasi-metric spaces. Such functions have interpol…