Besov spaces on fractals and tempered Radon measures [Elektronische Ressource] / Maryia Kabanava. Gutachter: Hans Triebel ; Martina Zähle ; Fernando Cobos Diaz

Besov spaces on fractals andtempered Radon measuresDissertationzur Erlangung des akademischen Gradesdoctor rerum naturalium (Dr. rer. nat.)vorgelegt dem Rat derFakulta¨t fu¨r Mathematik und Informatikder Friedrich-Schiller Universit¨at Jenavon M.Sc. Maryia Kabanavageboren am 16. Oktober 1984 in MinskGutachter1. Prof. Dr. Hans Triebel – summa cum laude2. Prof. Dr. Martina Z¨ahle – summa cum laude3. Prof. Dr. Fernando Cobos D´ıaz – summa cum laudeTag der ¨offentlichen Verteidigung: 26. Juli 2011AcknowledgementsI would like to express my deepest gratitude to my supervisors Professor Hans Triebeland Professor Hans-Ju¨rgen Schmeisser for many fruitful discussions, suggestions and re-marks. I would like to thank the whole group ”Function spaces” for inspiring and friendlyatmosphere. Besides, I would like to thank Professor Krotov for helpful conversationsand comments.ContentsZusammenfassung iiiIntroduction vii1 Preliminaries 11.1 Function spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Basic notation and classical Besov spaces . . . . . . . . . . . . . . 1s n1.1.2 Characterization of B (R ) by local means and atoms . . . . . . 2pq1.1.3 Weighted Besov spaces . . . . . . . . . . . . . . . . . . . . . . . . 41.1.4 Anisotropic Besov spaces . . . . . . . . . . . . . . . . . . . . . . . 5n1.1.5 Periodic Besov spaces onT . . . . . . . . . . . . . . . . . . . . . 71.1.6 Wavelets onR andT . . . . . . . . . . . . . . . . . . . . .