A study of weighted bergman projections
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A study of weighted bergman projections
UNIVERSITY OF [***] WOLLONGONG 10/A STUDYOFWEIGHTED BERGMAN PROJECTIONSPHUNG TRONG THƯCSupervisorsDr. Jiakun Liu and Dr. Iran Vu KhanhIllis thesis sub A study of weighted bergman projections bmitted in fulfilment for the requirements of the degreeDoctor of PhilosophyThe University of WollongongSchool of Mathematics and Applied Statistics43313DeclarationI. Phung Trong Thue, declare that this thesis submitted in fulfilment for the requirements of rhe degree Doctor of Philosophy, from the A study of weighted bergman projections University of Wollongong, is wholly my own work unless ot henvise referenced or acknowledged, rhe document has not been submitted for qualifications aA study of weighted bergman projections
t any other academic institution.Phung lYong Thue43313To my son, Phung Ha Nguyenand my wife, Ha Nguyen Thuy Linh.AbstractThe aim of t his thesis is toUNIVERSITY OF [***] WOLLONGONG 10/A STUDYOFWEIGHTED BERGMAN PROJECTIONSPHUNG TRONG THƯCSupervisorsDr. Jiakun Liu and Dr. Iran Vu KhanhIllis thesis sub A study of weighted bergman projections ult concerns estimates of weighted Bcrgnum kernels ami the holomorphic Hardy norm of the Bergman kernel. The main tools are L2-estimates of the ('/-equation and the relation between the Bergman kernel ami the pluricomplex Green function. In particular, these improve the result of Chen and Fu |CFH| o A study of weighted bergman projections n the comparison of the Szegd and Bergman kernels for the class of psemloconvex domains admitting a plurisubharmonic defining function, such as convexA study of weighted bergman projections
domains, strongly pseudoconvex domains and Kohn special domains.The second result extends the work of Cuckovic and McNeal |CM06j; and of Abate, RaissUNIVERSITY OF [***] WOLLONGONG 10/A STUDYOFWEIGHTED BERGMAN PROJECTIONSPHUNG TRONG THƯCSupervisorsDr. Jiakun Liu and Dr. Iran Vu KhanhIllis thesis sub A study of weighted bergman projections convex smooth domains in C", which we call sharp B-type domains, that contains such as strongly pseudoconvex domains in C", convex domains of finite type in C” and finite-type domains in c2.For the third result, we obtain the Lp mapping properties of the Bergman* Toeplitz operators (0.0.1) for a mod A study of weighted bergman projections el of non-smooth domains, namely, the fat Hartogs trianglesilt •*2) 6 c2 : |2j|* < |c2| < 1| > GAs a result, our work generalises the recent work by EA study of weighted bergman projections
dhohn ami McNeal ỊEM16Ị.AcknowledgementsIam indebted to my supervisors Dr. Jiakiin I.in and Dr. l¥an Vu Khanh for their guidance and encouragement timUNIVERSITY OF [***] WOLLONGONG 10/A STUDYOFWEIGHTED BERGMAN PROJECTIONSPHUNG TRONG THƯCSupervisorsDr. Jiakun Liu and Dr. Iran Vu KhanhIllis thesis sub A study of weighted bergman projections enjoyable view in doing research. They warmly support me in my family issues and also offer mo groat opport unities for attending international conferences throughout my time there.Special thanks to my housemates Ngo and True, and my friend Dave for their encouragement and friendship.1 would like to A study of weighted bergman projections thank Professor Dinh lien Cuong for the invitation to rhe complex geometry conference at NƯS in May 2017.I thank the referees for their thoughtful coA study of weighted bergman projections
mments, which help to improve the quality of this thesis.I am grateful to my family, especially my parents and my wife, who always encourage' and beliUNIVERSITY OF [***] WOLLONGONG 10/A STUDYOFWEIGHTED BERGMAN PROJECTIONSPHUNG TRONG THƯCSupervisorsDr. Jiakun Liu and Dr. Iran Vu KhanhIllis thesis subUNIVERSITY OF [***] WOLLONGONG 10/A STUDYOFWEIGHTED BERGMAN PROJECTIONSPHUNG TRONG THƯCSupervisorsDr. Jiakun Liu and Dr. Iran Vu KhanhIllis thesis subGọi ngay
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