In this talk, we study estimates for maximal functions and related problems in geometric measure theory or dispersive PDEs. We begin with Hardy-Littlewood maximal function and Lebesgue differentiation theorem. Then we consider spherical/circular maximal function and related problems in geometric measure theory. Also, we discuss the pointwise convergence problem in Schrodinger/wave equations, which are consequence of estimates for maximal function of propagators. To strengthen the results, we extend above-mentioned estimates to those relative to fractal measures.
일시: 9월 6일 (화) 16:40-17:10