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Multi-Dimensional Hardy Spaces

  • Ferenc Weisz
Chapter
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Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

In this chapter, two types of the multi-dimensional classical Hardy spaces, namely the \(H_{p}^{\square }(\mathbb{R}^{d})\) and \(H_{p}(\mathbb{R}^{d})\) spaces, are introduced. All the results of Chap.  1, amongst others, inequalities, atomic decompositions, interpolation theorems, boundedness results are proved for these spaces. Basically, the results for \(H_{p}^{\square }(\mathbb{R}^{d})\) are very similar to those for the one-dimensional \(H_{p}(\mathbb{R})\) spaces studied in Chap.  1, so we omit the corresponding proofs. However, the proofs for \(H_{p}(\mathbb{R}^{d})\) are different from the one-dimensional version requiring new ideas. We also study some generalizations of the Hardy-Littlewood maximal function for multi-dimensional functions.

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    For an up-to-date list of ANHA titles, please visit http://www.springer.com/series/4968

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Ferenc Weisz
    • 1
  1. 1.Department of Numerical AnalysisEötvös Loránd UniversityBudapestHungary

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