Characterizations of product Hardy spaces in Bessel setting

Xuan Thinh Duong, Ji Li, Brett D. Wick, Dongyong Yang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we work in the setting of Bessel operators and Bessel Laplace equations studied by Weinstein, Huber, and the harmonic function theory in this setting introduced by Muckenhoupt–Stein, especially the generalised Cauchy–Riemann equations and the conjugate harmonic functions. We provide the equivalent characterizations of product Hardy spaces associated with Bessel operators in terms of the Bessel Riesz transforms, non-tangential and radial maximal functions defined via Poisson and heat semigroups, based on the atomic decomposition, the generalised Cauchy–Riemann equations, the extension of Merryfield’s result which connects the product non-tangential maximal function and area function, and on the grand maximal function technique which connects the product non-tangential and radial maximal function. We then obtain directly the decomposition of the product BMO space associated with Bessel operators.
Original languageEnglish
Article number24
Pages (from-to)1-65
Number of pages65
JournalJournal of Fourier Analysis and Applications
Volume27
Issue number2
DOIs
Publication statusPublished - Apr 2021

Keywords

  • Bessel operator
  • maximal function
  • Littlewood-Paley theory
  • Bessel Riesz transform
  • Cauchy-Riemann type equations
  • Product Hardy space
  • Product BMO space

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