Graduation Year
2018
Date of Submission
4-2018
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Arts
Department
Mathematics
Reader 1
Winston Ou
Reader 2
Chiu-Yen Kao
Terms of Use & License Information
Abstract
In this thesis, we present the space BMO, the one-parameter Hardy-Littlewood maximal function, and the two-parameter strong maximal function. We use the John-Nirenberg inequality, the relation between Muckenhoupt weights and BMO, and the Coifman-Rochberg proposition on constructing A1 weights with the Hardy- Littlewood maximal function to show the boundedness of the Hardy-Littlewood maximal function on BMO. The analogous statement for the strong maximal function is not yet understood. We begin our exploration of this problem by discussing an equivalence between the boundedness of the strong maximal function on rectangular BMO and the fact that the strong maximal function maps A∞ weights into the A1 class. We then extend a multiparameter counterexample to the Coifman-Rochberg proposition proposed by Soria (1987) and discuss the difficulties in modifying it into an A∞ counterexample that would disapprove the boundedness of the strong maximal function.
Recommended Citation
Zhang, Wenhao, "The Boundedness of the Hardy-Littlewood Maximal Function and the Strong Maximal Function on the Space BMO" (2018). CMC Senior Theses. 1907.
https://scholarship.claremont.edu/cmc_theses/1907