On vector-valued tent spaces and Hardy spaces associated with non-negative self-adjoint operators

In this paper we study Hardy spaces associated with non-negative self-adjoint operators and develop their vector-valued theory. The complex interpolation scales of vector-valued tent spaces and Hardy spaces are extended to the endpoint p=1. The holomorphic functional calculus of L is also shown to be bounded on the associated Hardy space H^1_L(X). These results, along with the atomic decomposition for the aforementioned space, rely on boundedness of certain integral operators on the tent space T^1(X).Comment: 20 pages, references added, revised, to appear in Glasgow Mathematical Journa

Assessing effects of price regulation in retail payment systems

This paper considers effects of price regulation in retail payment systems by applying the model of tele-communications competition by Laffont-Rey-Tirole (1998). In our two-country model world there is one retail payment network located in each country and markets are segmented à la Hotelling. We show that the optimal price under price regulation is the weighted average of pre-regulation domestic and cross-border prices where the degree of home-bias in making payments serves as the weight. Furthermore, we find that the general welfare effects of price regulation are ambiguous: gross social welfare is higher un-der price discrimination than under price regulation in the special case where costs of access to banking services (transportation costs) are high. However, there also exist cases where prohibitively high transac-tion costs make price discrimination to reduce total welfare. Finally, if transportation costs are reduced sufficiently, segmentation of payment markets is eliminated. Markets then become fully-served as in the original Laffont-Rey-Tirole model, suggesting that price discrimination would be beneficial for welfare.payment systems; price regulation; retail payments

On the relation of Carleson's embedding and the maximal theorem in the context of Banach space geometry

Hyt\"onen, McIntosh and Portal (J. Funct. Anal., 2008) proved two vector-valued generalizations of the classical Carleson embedding theorem, both of them requiring the boundedness of a new vector-valued maximal operator, and the other one also the type p property of the underlying Banach space as an assumption. We show that these conditions are also necessary for the respective embedding theorems, thereby obtaining new equivalences between analytic and geometric properties of Banach spaces.Comment: 11 pages, typos corrected, proof of Theorem 2 revise