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Jovanović Spasojević, Tanja (Beograd , 2022)[more][less]
Abstract: In this thesis, subjects of consideration are the embeddings theorems of weighted Bergman spaces in Lp-spaces, as well as embeddings theorems of harmonic mixed norm spaces. The first part of the thesis generalizes the theorems of embeddings Bergman spaces into Lp(μ)-spaces, where μ is a Borel measure on a given domain. They have been earlier studied on domains such as unit ball and upper half-space. Generalization refers to bounded domains Ω ⊂ Rn with C1 boundary. This embedding will be valid to any p > 0, whenever the measure of the spaces Lp satisfies the Carledon condition. Reverse the direction will be valid only in case if p > 1 + α+2 n−2 . The second part of the dissertation also generalizes the embeddings theorems of mixed norm spaces of harmonic functions on a unit ball, where the generalization is applied to the domain Ω ⊂ Rn with C1 boundary. However, in addition we are obtaining another important result relating to the limitation of the maximum operators in the mixed norm on the general domain for the class of QNS functions. URI: http://hdl.handle.net/123456789/5378 Files in this item: 1
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