Multi-Dimensional hardy spaces

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this chapter, two types of the multi-dimensional classical Hardy spaces, namely the Hp (ℝd) and Hp(ℝd) 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 Hp (ℝd) are very similar to those for the one-dimensional Hp(ℝ) spaces studied in Chap. 1, so we omit the corresponding proofs. However, the proofs for Hp(ℝd) 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.

Original languageEnglish
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Pages137-202
Number of pages66
Edition9783319568133
DOIs
Publication statusPublished - Jan 1 2017

Publication series

NameApplied and Numerical Harmonic Analysis
Number9783319568133
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

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ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Weisz, F. (2017). Multi-Dimensional hardy spaces. In Applied and Numerical Harmonic Analysis (9783319568133 ed., pp. 137-202). (Applied and Numerical Harmonic Analysis; No. 9783319568133). Springer International Publishing. https://doi.org/10.1007/978-3-319-56814-0_3