Style transfer is a central problem of machine learning with numerous successful applications. In this work, we present a novel style transfer framework building upon infinite task learning and vector-valued reproducing kernel Hilbert spaces. We consider style transfer as a functional output regression task where the goal is to transform the input objects to a continuum of styles. The learnt mapping is governed by the choice of two kernels, one on the object space and one on the style space, providing flexibility to the approach. We instantiate the idea in emotion transfer where facial landmarks play the role of objects and styles correspond to emotions. The proposed approach provides a principled way to gain explicit control over the continuous style space, allowing to transform landmarks to emotions not seen during the training phase. We demonstrate the efficiency of the technique on popular facial emotion benchmarks, achieving low reconstruction cost.