Heat kernels for time-dependent non-symmetric mixed L?vy-type operators

In this paper we establish the existence, uniqueness and reg-ularity of heat kernels to a large class of time-inhomogeneous non-symmetric nonlocal operators with Dini's continuous ker-nels. Moreover, quantitative estimates including two-sided es-timates, gradient and fractional derivative estimates of the heat kernels are obtained. (c) 2023 Elsevier Inc. All rights reserved.