Product Hardy spaces associated to operators with heat kernel bounds on spaces of homogeneous type

The aim of this article is to develop the theory of product Hardy spaces associated with operators which possess the weak assumption of Davies--Gaffney heat kernel estimates, in the setting of spaces of homogeneous type. We also establish a Calder\'on--Zygmund decomposition on product spaces, which is of independent interest, and use it to study the interpolation of these product Hardy spaces. We then show that under the assumption of generalized Gaussian estimates, the product Hardy spaces coincide with the Lebesgue spaces, for an appropriate range of~$p$.Comment: Accepted by Math.

Sublattice-sensitive Majorana Modes

For two- and three-dimensional topological insulators whose unit cells consist of multiple sublattices, the boundary terminating at which type of sublattice can affect the time-reversal invariant momentum at which the Dirac points of helical boundary states are located. Through a general theory and a representative model, we reveal that this interesting property allows the realization of Majorana modes at sublattice domain walls forming on the boundary when the boundary Dirac points of the topological insulator are gapped by an unconventional superconductor in proximity. Intriguingly, we find that the sensitive sublattice-dependence of the Majorana modes allows their positions to be precisely manipulated by locally controlling the terminating sublattices or boundary potential. Our work reveals that the common sublattice degrees of freedom in materials open a new route to realize and manipulate Majorana modes.Comment: 21 pages,10 figure

Variability in the impacts of partisan conflict: a new perspective from bank credit

The purpose of this article is to analyse the impact of partisan conflict on bank credit, and take the global financial crisis as the time node to analyse the variability of this impact before and after the financial crisis. This article examines the impacts of partisan conflict on the bank credit by employing the US data covering the past 40 years and captures the variability in the effects of partisan conflict based on the rolling sample and time-varying parameter VAR analysis. The full sample results reveal that one standard deviation partisan conflict shock will shrink the bank credit growth rate to nonfinancial sectors, and the negative effects of partisan conflict on bank credit are more substantial after the global financial crisis. The rolling sample and time-varying parameter VAR analysis further confirm that the impacts of partisan conflict shock have varied substantially over time, where bank credit still negatively reacts to the impacts of partisan conflict in recent periods. Additionally, we estimate two extended models and support the intermediate role of economic policy uncertainty in transmitting the partisan conflict and the substitution effect of cross-border bank lending on domestic bank credit. Finally, our major results are unchanged by performing a series of robustness checks. The conclusion of this article is that partisan conflict has a significant impact on bank credit and shows obvious variability, which is more significant after the global financial crisis