The Green formula and HP Spaces on trees.
The Pick problem and the Cole-Lewis-Wermer theorem.
The Pick problem in and and the Cole-Lewis-Wermer problem.
The structure of the Haar systems on locally compact groupoids.
Triebel-Lizorkin spaces with non-doubling measures
Suppose that μ is a Radon measure on , which may be non-doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀ > 0 such that for all x ∈ supp(μ) and r > 0, μ(B(x,r)) ≤ C₀rⁿ, where 0 < n ≤ d. The authors provide a theory of Triebel-Lizorkin spaces for 1 < p < ∞, 1 ≤ q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure μ, C₀, n and d. The method does not use the vector-valued maximal function inequality...
Type-dependent positive definite functions on free products of groups