Ben Krause

Multi-Frequency Oscillation Estimates Arising in Pointwise Ergodic Theory

Abstract We prove essentially optimal $$L^p(\mathbb {R})$$ L p ( R ) -estimates for variational variants of the maximal Fourier multiplier operators considered by Bourgain in his work on pointwise convergence of polynomial ergodic averages. As a corollary of our methods, we are a...