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Orlicz Spaces and Generalized Orlicz Spaces

  • Petteri Harjulehto
  • Peter Hästö

Part of the Lecture Notes in Mathematics book series (LNM, volume 2236)

Table of contents

  1. Front Matter
    Pages i-x
  2. Petteri Harjulehto, Peter Hästö
    Pages 1-12
  3. Petteri Harjulehto, Peter Hästö
    Pages 13-46
  4. Petteri Harjulehto, Peter Hästö
    Pages 47-78
  5. Petteri Harjulehto, Peter Hästö
    Pages 79-103
  6. Petteri Harjulehto, Peter Hästö
    Pages 105-121
  7. Petteri Harjulehto, Peter Hästö
    Pages 123-144
  8. Petteri Harjulehto, Peter Hästö
    Pages 145-157
  9. Back Matter
    Pages 159-169

About this book

Introduction

This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a technique centered on the use of equivalent Φ-functions. Results from classical functional analysis are presented in detail and new material is included on harmonic analysis. Extrapolation is used to prove, for example, the boundedness of Calderón–Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and Sobolev–Poincaré inequalities in norm and modular forms.

Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.


Keywords

Extrapolation Maximum Function Musielak-Orlicz Space Orlicz Space Phi-function Sobolev Space

Authors and affiliations

  • Petteri Harjulehto
    • 1
  • Peter Hästö
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland
  2. 2.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-15100-3
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-15099-0
  • Online ISBN 978-3-030-15100-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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