Parabolic Muckenhoupt weights in the Euclidean space

We introduce a parabolic analogue of Muckenhouptʼs A p class. We show that these weights satisfy a reverse Hölder type inequality and also prove a John–Nirenberg inequality for a related BMO type class. Both results are multidimensional generalizations of known one-dimensional results. As an application of our methods, we extend a two-dimensional weighted norm inequality of A. Lerner and S. Ombrosi to dimensions n ⩾ 3 .