Weighted function spaces and traces on fractals [Elektronische Ressource] / von Iwona Piotrowska

Weighted function spaces and traces onfractalsDissertationzur Erlangung des akademischen Gradesdoctor rerum naturalium (Dr. rer. nat.)vorgelegt dem Rat derFakult¨at fu¨r Mathematik und Informatikder Friedrich-Schiller-Universit¨at Jenavon Dipl.-Math. Iwona Piotrowskageboren am 06. Juni 1980 in Cz luch´owGutachter1. PD Dr. Dorothee D. Haroske2. Prof. Dr. Hans Triebel3. Prof. Dr. Miroslav KrebecTag der letzten Pru¨fung des Rigorosums: 23.10.2006Tag der o¨ffentlichen Verteidigung: 03.11.2006AcknowledgementsFirst of all I wish to express my deepest appreciation to my supervisor PD Dr.Dorothee D. Haroske. I am greatly indebted to her for many stimulating conversa-tions, suggestions and remarks. I also would like to thank Prof. Dr. Hans Triebelfor the helpful discussions and suggestions. I thank Prof. Dr. Miroslav Krbec, PDDr. Dorothee D. Haroske and Prof. Dr. Hans Triebel for kindly agreeing to serveas referee for this thesis. I also thank Mariusz Piotrowski for his permanent supportand remarks. Further, I thank the following individuals for useful discussions andcomments: Jan Schneider and Steffen Winter.Finally, I wish to thank the Junior Research Team ”Fractal Analysis” for financialsupport.Contents1 Introduction 102 Preliminaries 132.1 Notation and conventions . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Classical function spaces . . . . . . . . . . . . . . . . . . . . . . . . . 152.3 Muckenhoupt weights . . . . . . . . . . . . . . . . .