Real-Variable Theory of Musielak-Orlicz Hardy Spaces

The main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of MusielakOrlicz Hardy-type function spaces, and to lay the foundations for further applications.

The real-variable theory of function spaces has always been at the core of harmonic analysis. Recently, motivated by certain questions in analysis, some more general MusielakOrlicz Hardy-type function spaces were introduced. These spaces are defined via growth functions which may vary in both the spatial variable and the growth variable. By selecting special growth functions, the resulting spaces may have subtler and finer structures, which are necessary in order to solve various endpoint or sharp problems.

This book is written for graduate students and researchers interested in function spaces and, in particular, Hardy-type spaces.

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• Detailed and complete real-variable theory of Musielak-Orlicz Hardy type function spaces Detailed and self-contained arguments for the main results Presents some applications to endpoint or sharp problems of analysis Detailed references and more known related results of each chapter Includes supplementary material: sn.pub/extras

  Inhalt
  Preface. - 1 Musielak-Orlicz Hardy Spaces. - 2 Maximal Function Characterizations of Musielak-Orlicz Hardy Spaces. - 3 Littlewood-Paley Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces. - 4 Riesz Transform Characterizations of Musielak-Orlicz Hardy Spaces.- 5 Musielak-Orlicz Campanato Spaces. - 6 Intrinsic Square Function Characterizations of Musielak-Orlicz Hardy Spaces. - 7 Weak Musielak-Orlicz Hardy Spaces. - 8 Local Musielak-Orlicz Hardy Spaces.