Topics in Littlewood-Paley theory and BMO
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] In this thesis we discuss some important results in Littlewood-Paley theory and the space of Bounded-Mean Oscillation functions, henceforth called BMO. Littlewood-Paley Theory has its roots in the Littlewood-Paley Theorem, which is essentially an extension of Plancherel's identity for higher order Lebesgue spaces. The most fundamental results in Littlewood-Paley theory are presented in this thesis, as well as applications in the theory of multipliers and PDEs. The space BMO consists of locally integrable functions whose oscillation is controlled in the mean sense. Some non-trivial facts about this space are shown in this work, as well as some applications in measure theory.
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