Two-weight norm inequalities for parabolic fractional maximal functions

Abstract: We prove two-weight norm inequalities for parabolic fractional maximal functions using parabolic Muckenhoupt weights. In particular, we prove a two-weight, weak-type estimate and Fefferman-Stein type inequalities for the centered parabolic maximal function. We also prove that a parabolic Sawyer-type condition implies the strong-type estimate for the parabolic fractional maximal function. Finally, we prove the strong-type estimate for the centered parabolic maximal function assuming a stronger parabolic Muckenhoupt bump condition.