110 citations · 529 across the 44 of their papers we have counts for
22 papers · 1 filter
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 and establish the quantitative boundedness of several operators on local matrix-we…
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 supporting a Poincaré inequality, we prove weak-type characterizations of the Sobolev space and the spac…
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…
New Characterizations and Properties of Matrix Weights
Fan Bu, Tuomas Hytönen, Dachun Yang +1
We provide several new characterizations of -matrix weights, originally introduced by A. Volberg as matrix-valued substitutes of the classical weights. In…
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…
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…
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…
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…
Extrapolation of compactness on weighted spaces
Tuomas Hytönen, Stefanos Lappas
Let be a linear operator that, for some , is bounded on for all and in addition compact on $L^{p_1}(w_1…
The space : nontriviality and duality
Galia Dafni, Tuomas Hytönen, Riikka Korte +1
We study a function space based on a condition introduced by John and Nirenberg as a variant of BMO. It is known that , but otherwi…
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 and theorems. In particular, we obtain the non-homogeneous theorem under weaker kernel reg…
Vector-valued local approximation spaces
Tuomas Hytönen, Jori Merikoski
We prove that for every Banach space , the Besov spaces of functions from the -dimensional Euclidean space to agree with suitable local approximation spaces with equivale…
Heat flow and quantitative differentiation
Tuomas Hytönen, Assaf Naor
For every Banach space that admits an equivalent uniformly convex norm we prove that there exists with the following property. Suppose that…
Quantitative affine approximation for UMD targets
Tuomas Hytönen, Sean Li, Assaf Naor
It is shown here that if is a Banach space in which martingale differences are unconditional (a UMD Banach space) then there exists with th…
Pisier's inequality revisited
Tuomas Hytönen, Assaf Naor
Given a Banach space , for and we investigate the smallest constant for which every sa…
Pointwise convergence of vector-valued Fourier series
Tuomas P. Hytönen, Michael T. Lacey
We prove a vector-valued version of Carleson's theorem: Let Y=[X,H]_t be a complex interpolation space between a UMD space X and a Hilbert space H. For p\in(1,\infty) and f\in L^p(…
Stability in p of the H-infinity calculus of first-order systems in L^p
Tuomas Hytönen, Alan McIntosh
We study certain differential operators of the form AD arising from a first-order approach to the Kato square root problem. We show that if such operators are R-bisectorial in L^p,…
On the relation of Carleson's embedding and the maximal theorem in the context of Banach space geometry
Tuomas Hytönen, Mikko Kemppainen
Hytönen, McIntosh and Portal (J. Funct. Anal., 2008) proved two vector-valued generalizations of the classical Carleson embedding theorem, both of them requiring the boundedness of…
Non-homogeneous Tb theorem and random dyadic cubes on metric measure spaces
Tuomas Hytönen, Henri Martikainen
We prove a Tb theorem on quasimetric spaces equipped with what we call an upper doubling measure. This is a property that encompasses both the doubling measures and those satisfyin…
The Littlewood--Paley--Rubio de Francia property of a Banach space for the case of equal intervals
T. P. Hytönen, J. L. Torrea, D. V. Yakubovich
Let be a Banach space. It is proved that an analogue of the Rubio de Francia square function estimate for partial sums of the Fourier series of -valued functions holds true…
Diagonalization and representation results for nonpositive sesquilinear form measures
Tuomas Hytonen, Juha-Pekka Pellonpaa, Kari Ylinen
We study decompositions of operator measures and more general sesquilinear form measures into linear combinations of positive parts, and their diagonal vector expansions. The u…
Positive sesquilinear form measures and generalized eigenvalue expansions
Tuomas Hytönen, Juha-Pekka Pellonpää, Kari Ylinen
Positive operator measures (with values in the space of bounded operators on a Hilbert space) and their generalizations, mainly positive sesquilinear form measures, are considered…