4 papers
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…
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…
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…