Hausdorff operators on modulation and Wiener amalgam spaces

We give the sharp conditions for boundedness of Hausdorff operators on certain modulation and Wiener amalgam spaces.Comment: To appear in "Annals of Functional Analysis

Integral restriction for bilinear operators

We consider the integral domain restriction operator TΩ for certain bilinear operator T. We obtain that if (s, p1, p2) satisfies 1 p1+ 1 p2 ≥ 2 min{1,s} and kTkLp1 ×Lp2→Ls 1 min{1,s}

A Conditional Variational Framework for Dialog Generation

Deep latent variable models have been shown to facilitate the response generation for open-domain dialog systems. However, these latent variables are highly randomized, leading to uncontrollable generated responses. In this paper, we propose a framework allowing conditional response generation based on specific attributes. These attributes can be either manually assigned or automatically detected. Moreover, the dialog states for both speakers are modeled separately in order to reflect personal features. We validate this framework on two different scenarios, where the attribute refers to genericness and sentiment states respectively. The experiment result testified the potential of our model, where meaningful responses can be generated in accordance with the specified attributes.Comment: Accepted by ACL201