题 目: Parabolic weighted norm inequalities
报告人：Professor Juha Kalevi Kinnunen (University of Aalto, Finland)
地 点: 后主楼1124室
摘 要: We discuss parabolic Muckenhoupt weights and functions of bounded mean oscillation (BMO) related to a doubly nonlinear parabolic partial differential equation. In the natural geometry for the doubly nonlinear equation the time variable scales as the modulus of the space variable raised to a power. Consequently the Euclidean balls and cubes have to be replaced by parabolic rectangles respecting this scaling in all estimates. An extra challenge is given by the time lag appearing in the estimates. The main result gives a full characterization of weak and strong type weighted norm inequalities for parabolic forward in time maximal operators. In addition, we give a Jones type factorization result for the parabolic Muckenhoupt weights and a Coifman-Rochberg type characterization of the parabolic BMO through parabolic Muckenhoupt weights and maximal functions. We also discuss connections and applications of the results to regularity of nonlinear parabolic partial differential equations.