Hinčinova neenakost : delo diplomskega seminarja

Brešar, Miha (author), Dragičević, Oliver (mentor)

Hinčinova neenakost spada med klasične neenakosti. Čeprav velja za verjetnostno neenakost, se pogosto uporablja tudi v analizi. V diplomskem delu ob dokazu neenakosti predstavimo nekatere lastnosti Schwartzovega prostora in Fourierovih transformacij, s katerimi v zaključku dokažemo Littlewood-Paleyev izrek, ki velja za enega temelnjih izrekov v harmonični analizi.

• Language: Slovenian
• Keywords: Hinčinova neenakost, Fourierova transformacija, Schwartzov prostor, Littlewood-Paleyev izrek
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2019
• PID: 20.500.12556/RUL-109339
• UDC: 517
• COBISS.SI-ID: 18710617
• Publication date in RUL: 30.08.2019

Secondary language

• Language: English
• Title: Khintchine's inequality

Abstract

Khintchine inequality is one of the classical inequalities. Even though it is considered a probabilistic inequality, we find most of its applications in analysis. In this diploma thesis, along with the proof of the inequality we present some properties of Schwartz spaces and the Fourier transform, that we use to prove the Littlewood-Paley theorem, which is one of fundamental theorems of harmonic analysis.

• Keywords: Khintchine inequality, Fourier transform, Schwartz space, Littlewood- Paley theorem