$H^1$-BMO duality on graphs

Bellman Function and the H 1 − BMO Duality

The emergence in the past decade of the Bellman function method as a powerful and versatile harmonic analysis technique has been characterized by rapid theoretical development on the one hand and somewhat ad hoc, if effective, approaches to some problems on the other. From the groundbreaking applications in [NTV1, NT, NTV2], which put the method on the map, to the concerted effort at tracing it...

On bounded treewidth duality of graphs

Graphs, Links, and Duality on Surfaces

We introduce a polynomial invariant of graphs on surfaces, PG , generalizing the classical Tutte polynomial. Topological duality on surfaces gives rise to a natural duality result for PG , analogous to the duality for the Tutte polynomial of planar graphs. This property is important from the perspective of statistical mechanics, where the Tutte polynomial is known as the partition function of t...

BMO ON STRONGLY PSEUDOCONVEX DOMAINS: HANKEL OPERATORS, DUALITY AND a-ESTIMATES

We study the condition that characterizes the symbols of bounded Hankel operators on the Bergman space of a strongly pseudoconvex domain and show that it is equivalent to BMO plus analytic. (Here we mean the Bergman metric BMO of Berger, Coburn and Zhu.) In the course of the proof we obtain new d -estimates that may be of independent interest. Some applications include a decomposition of BMO si...

Duality of Infinite Graphs

Some basic results on duality of infinite graphs are established and it is proven that a block has a dual graph if and only if it is planar and any two vertices are separated by a finite edge cut. Also, the graphs having predual graphs are characterized completely and it is shown that if G* is a dual and predual graph of G, then G and G* can be represented as geometric dual graphs. The uniquene...