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…
Besov--Triebel--Lizorkin-Type Spaces with Matrix Weights
Fan Bu, Tuomas Hytönen, Dachun Yang +1
Introduced by A. Volberg, matrix weights provide a suitable generalization of Muckenhoupt weights from the classical theory. In our previous work, we esta…
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…
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…