Stipčić, Mario (2015) Valićne karakterizacije Soboljevljevih prostora. Diploma thesis, Faculty of Science > Department of Mathematics.

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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.
Item Type:  Thesis (Diploma thesis) 

Supervisor:  Kovač, Vjekoslav 
Date:  2015 
Number of Pages:  39 
Subjects:  NATURAL SCIENCES > Mathematics 
Divisions:  Faculty of Science > Department of Mathematics 
Depositing User:  Iva Prah 
Date Deposited:  27 Oct 2015 11:09 
Last Modified:  27 Oct 2015 11:09 
URI:  http://digre.pmf.unizg.hr/id/eprint/4316 
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