Procene gradijenta funkcija i normi operatora u teoriji harmonijskih funkcija

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Procene gradijenta funkcija i normi operatora u teoriji harmonijskih funkcija

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dc.contributor.advisor Arsenović, Miloš
dc.contributor.author Melentijević, Petar
dc.date.accessioned 2018-12-24T16:40:43Z
dc.date.available 2018-12-24T16:40:43Z
dc.date.issued 2018
dc.identifier.uri http://hdl.handle.net/123456789/4749
dc.description.abstract In this thesis we study sharp estimates of gradients and operator norm estimates in harmonic function theory. First, we obtain Schwarz-type inequalities for holomorphic mappings from the unit ball B n to the unit ball B m , and then analoguous inequalities for holomorphic functions on the disk D without zeros and pluriharmonic functions from the unit ball B n to ( − 1 , 1) . These extend results from [ 32 ] and [ 18 ]. Also, we give a new proof of the fact that positive harmonic function in the upper-half plane is a contraction with resprect to hyperbolic metrics on both H and R + ([ 47 ]). Besides that, in the second chapter, we construct the examples to show that the analoguous does not hold for the higher-dimensional upper-half spaces. All mentioned results are from the authors’ paper [55]. In the third chapter we intend to calculate the exact seminorm of the weighted Berezin transform considered as an operator from L ∞ ( B n ) to the ”smooth” Bloch space ([57]). The fourth chapter contains results concerning Bergman projection. We solve the problem posed by Kalaj and Marković in [ 28 ] on determining the exact seminorm of the Bergman projections from L ∞ ( B n ) to the B ( B n ) . The crucial obstacle is the fact that B ( B n ) is equipped with M− invariant gradient seminorm. Also, we provide the sharp gradient estimates of the Bergman projection of an L p function in the unit ball B n , as well as its consequences on Cauchy projection and certain gradient estimates for the functions from the Hardy and Bergman spaces.We obtain the exact values of the Bloch’s seminorms and norms for the Cauchy projection on L ∞ ( S n ) . These results are based on the papers [56] and [58]. The last chapter contains the proof of the one part of Hollenbeck-Verbitsky conjecture from [ 26 ]. Exactly, we find the exact norms of ( | P + | s + | P − | s ) 1 s for 0 < s ≤ 2 on L p ( T ) , where P + is the Riesz projection and P − = I − P + . Also we give the appropriate dual estimates and prove that they are sharp. The paper [ 45 ] is motivated by the results from [25] and [33]. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2018-12-24T16:40:43Z No. of bitstreams: 1 doktorat_Petar_merged.pdf: 1507835 bytes, checksum: 9d09d7334be314f521272f82c991d956 (MD5) en
dc.description.provenance Made available in DSpace on 2018-12-24T16:40:43Z (GMT). No. of bitstreams: 1 doktorat_Petar_merged.pdf: 1507835 bytes, checksum: 9d09d7334be314f521272f82c991d956 (MD5) Previous issue date: 2018 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title Procene gradijenta funkcija i normi operatora u teoriji harmonijskih funkcija en_US
mf.author.birth-date 1989-05-09
mf.author.birth-place Užice en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srbin en_US
mf.subject.area Mathematics en_US
mf.subject.keywords Schwarz lemma, Bergman projection, Berezin transform, Riesz projection, Hardy space, Bergman space, Bloch space en_US
mf.subject.subarea Complex analysis en_US
mf.contributor.committee Arsenović, Miloš
mf.contributor.committee Mihić, Olivera
mf.contributor.committee Jocić, Danko
mf.university.faculty Mathematics faculty en_US
mf.document.references 85 en_US
mf.document.pages 119 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.university Belgrade en_US

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