Oscillation inequalities for rectangles
In this paper we extend previously obtained results on If norm inequalities (1 < p < co) for square functions, oscillation and variation operators, with Z actions, to the case of Zd actions. The technique involves the use of a result about vector valued maximal functions, due to Fefferman and Stein, to reduce the problem to a situation where we can apply our previous results. ©2000 American Mathematical Society.
Proceedings of the American Mathematical Society
Jones, R., Rosenblatt, J., & Wierdl, M. (2001). Oscillation inequalities for rectangles. Proceedings of the American Mathematical Society, 129 (5), 1349-1358. https://doi.org/10.1090/s0002-9939-00-06032-9