110 citations · 529 across the 44 of their papers we have counts for
8 papers · 1 filter
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…
Pisier's inequality revisited
Tuomas Hytönen, Assaf Naor
Given a Banach space , for and we investigate the smallest constant for which every sa…
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…
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(…
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…