LITTLEWOOD-PALEY THEOREM FOR FUNCTION IN REAL AND IN LEBESGUE SPACE - Setiawan, David
The Lebesgue spaces are functions spaces that have many applications, from statistic, quantum mechanics to stochastic calculus. Fourier transform play a role in changing a variable into another variable, particularly frequency. The Lebesgue spaces and Fourier transform can solve various questions in harmonic analysis. However to understand both, we need characterizations that are sometimes complicated to explain. In consequence, equivalence properties are needed which can make it easier to investigate its properties. Littlewood-Paley g function is a function that can represent and help understand Lebesgue space. This research systematically discusses proof of norm equivalence property in the Lebesgue space between a function and Littlewood-Paley g function, proven through Calderón-Zygmund theorem.