Browsing Doctoral Dissertations by Author "Marković, Marijan"
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Marković, Marijan (Belgrade , 2013)[more][less]
Abstract: This work consists of three chapters. The first one contains some well known facts about Hardy classes of harmonic, analytic, and logarithmically subharmonic functions in the unit disk, as well as their applications. Then we briefly talk about the harmonic and minimal surfaces, the classical isoperimetric inequality, and the more recent results related to this inequality. One of the most elegant way to establish the isoperimetric inequality is via Carleman’s inequality for analytic functions in disks. In the second chapter we present the results from our recent work [29] for harmonic mappings of a disc onto a Jordan surface. In this chapter we establish the versions of classical theorems of Carath´eodory and Smirnov for mappings of the previous type. At the end of the head we apply these results to prove the isoperimetric inequality for Jordan harmonic surfaces bounded by rectifiable curves. In the third chapter, according to the author paper [35], we prove an inequality of the isoperimetric type, similar to Carleman’s, for functions of several variables. The first version of this inequality is for analytic functions in a Reinhardt domain. The second one concerns the functions that belong to Hardy spaces in polydiscs. URI: http://hdl.handle.net/123456789/2586 Files in this item: 1
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