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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id-itb.:478512020-06-22T13:24:51ZLITTLEWOOD-PALEY THEOREM FOR FUNCTION IN REAL AND IN LEBESGUE SPACE Setiawan, David Indonesia Final Project Lebesgue Spaces, Fourier Transform, Calderón-Zygmund, Littlewood-Paley g function INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/47851 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. text |
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Indonesia Indonesia |
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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. |
| format |
Final Project |
| author |
Setiawan, David |
| spellingShingle |
Setiawan, David LITTLEWOOD-PALEY THEOREM FOR FUNCTION IN REAL AND IN LEBESGUE SPACE |
| author_facet |
Setiawan, David |
| author_sort |
Setiawan, David |
| title |
LITTLEWOOD-PALEY THEOREM FOR FUNCTION IN REAL AND IN LEBESGUE SPACE |
| title_short |
LITTLEWOOD-PALEY THEOREM FOR FUNCTION IN REAL AND IN LEBESGUE SPACE |
| title_full |
LITTLEWOOD-PALEY THEOREM FOR FUNCTION IN REAL AND IN LEBESGUE SPACE |
| title_fullStr |
LITTLEWOOD-PALEY THEOREM FOR FUNCTION IN REAL AND IN LEBESGUE SPACE |
| title_full_unstemmed |
LITTLEWOOD-PALEY THEOREM FOR FUNCTION IN REAL AND IN LEBESGUE SPACE |
| title_sort |
littlewood-paley theorem for function in real and in lebesgue space |
| url |
https://digilib.itb.ac.id/gdl/view/47851 |
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1822271563478597632 |