Generalized 2-microlocal Besov spaces [Elektronische Ressource] / eingereicht von Henning Kempka

Generalized 2-microlocal Besov spacesDissertationzur Erlangung des akademischen Gradesdoctor rerum naturalium (Dr. rer. nat.)vorgelegt dem Rat der Fakult˜at fur˜ Mathematik und Informatik derFriedrich-Schiller-Universit˜at Jenaeingereicht von Dipl. Math. Henning Kempkageboren am 22.05.1979 in JenaGutachter1. Prof. Hans-Jurgen˜ Schmei…er2. Prof. Hans-Gerd Leopold3. Prof. Miroslav KrbecTag der letzten Prufung˜ des Rigorosums: 27. Juni 2008Tag der ˜ofientlichen Verteidigung: 1. Juli 2008AcknowledgementI am deeply grateful to my supervisor Prof. Hans-Jurgen˜ Schmei…er for many sugges-tions, patience and continued support. In addition, I would like to thank the entirescientiflc group "Funktionenr˜aume" of the Friedrich-Schiller University in Jena. I al-ways appreciated communication and the encouraging atmosphere.I owe special thanks to Prof. Hans Triebel for many valuable discussions and his insightand to Dr. Jan Vybiral for corrections and his friendship.Contents1 Introduction 7s;mloc n2 The 2-microlocal Besov spaces B (R ;w) 11pq2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Deflnitions and basic properties . . . . . . . . . . . . . . . . . . . . . . . 122.3 Fourier multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4 Lift property and equivalent norms . . . . . . . . . . . . . . . . . . . . . 202.5 Embedding theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.5.