Title: Valićne karakterizacije Soboljevljevih prostora
Abstract: This thesis deals with the proofs of characterizations of inhomogeneous and homogeneous Sobolev spaces expressed through the coefficients of a function, or in general a distribution, in an appropriate wavelet basis. Along with the introduction of notions of a wavelet basis and Sobolev spaces, some other basic objects are defined and the results and proofs needed in the thesis are given. The statement and the proof of the characterization of the Lebesgue space \(L^p (\mathbb{R}^n)\) is given. Along with that result the characterizations of inhomogeneous Sobolev space \(W^{p,s} (\mathbb{R}^n)\) expressed through coefficients in two types of wavelet systems are established and then also the characterization of the homogeneous Sobolev space \(\mathring{W}^{p,s} (\mathbb{R}^n)\) is given.
Publication Year: 2015
Publication Date: 2015-09-23
Language: en
Type: dissertation
Access and Citation
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot