Topics in dyadic Dirichlet spaces.
Exponential integrability of certain singular integral transforms
The Dirichlet space: a survey.
Compensated compactness and the Heisenberg group.
Compensated compactness and the Heisenberg group.
Factorization of the Green's operator and weak-type estimates for a random walk on a tree.
Orthogonal polynomials and middle Hankel operators on Bergman spaces
We introduce a sequence of Hankel style operators , k = 1,2,3,..., which act on the Bergman space of the unit disk. These operators are intermediate between the classical big and small Hankel operators. We study the boundedness and Schatten-von Neumann properties of the and show, among other things, that are cut-off at 1/k. Recall that the big Hankel operator is cut-off at 1 and the small Hankel operator at 0.
Carleson measures for analytic Besov spaces.
We characterize Carleson measures for the analytic Besov spaces. The problem is first reduced to a discrete question involving measures on trees which is then solved. Applications are given to multipliers for the Besov spaces and to the determination of interpolating sequences. The discrete theorem is also applied to analysis of function space on trees.
Hankel forms and the Fock space.
Page 1