LITTLEWOOD-PALEY THEOREM FOR FUNCTION IN REAL AND IN LEBESGUE SPACE
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...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/47851 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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