Harmonic functions, conjugate harmonic functions and the Hardy space H¹ in the rational Dunkl setting

2018/02/19 by Jean-Philippe Anker, Jacek Dziubański, Anker, Jean-Philippe +3
Mathematics · #Mathematical Analysis and Transform Methods #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1802.06607

Abstract

In this work we extend the theory of the classical Hardy space H¹ to the rational Dunkl setting. Specifically, let Δ be the Dunkl Laplacian on a Euclidean space ℝ^N. On the half-space ℝ₊×ℝ^N, we consider systems of conjugate (∂_t²+Δ_x)-harmonic functions satisfying an appropriate uniform L¹ condition. We prove that the boundary values of such harmonic functions, which constitute the real Hardy space H¹, can be characterized in several different ways, namely by means of atoms, Riesz transforms, maximal functions or Littlewood-Paley square functions.

Citations

• Some new function spaces and their applications to Harmonic analysis
• Hp spaces of several variables

Related

• Hardy spaces for the Dunkl harmonic oscillator
• The Hardy space H1 in the rational Dunkl setting
• Harmonic analysis operators in the rational Dunkl settings
• Remark on atomic decompositions for Hardy space H¹ in the rational\n Dunkl setting
• Hilbert transform on the Dunkl-Hardy Spaces