Riesz transforms, Cauchy-Riemann systems and amalgam Hardy spaces

Al Tarazi Assaubay, Jorge J. Betancor, Alejandro J. Castro, Juan C. Fariña

Research output: Contribution to journalArticlepeer-review


In this article we study Hardy spaces ℋp,q(ℝd), 0 < p, q < ∞, modeled over amalgam spaces (Lp, ℓq)(ℝd). We characterize ℍp,q(ℝd) by using first-order classical Riesz transforms and compositions of first-order Riesz transforms, depending on the values of the exponents p and q. Also, we describe the distributions in Hp, q(ℝd) as the boundary values of solutions of harmonic and caloric Cauchy-Riemann systems. We remark that caloric Cauchy-Riemann systems involve fractional derivatives in the time variable. Finally, we characterize the functions in L2(ℝd) ∪ Hp, q(ℝd) by means of Fourier multipliers mθ with symbol θ(·=/| · |), where θ ∈ C∞ (Sd-1) and Sd-1 denotes the unit sphere in ℝd

Original languageEnglish
Pages (from-to)697-725
Number of pages29
JournalBanach Journal of Mathematical Analysis
Issue number3
Publication statusPublished - Jan 1 2019


  • Amalgam spaces
  • Cauchy-Riemann equations
  • Hardy spaces
  • Riesz transforms

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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