Hilbert transform on the Dunkl-Hardy Spaces

2022/06/29 by Hu, ZhuoRan
#42A38 #42B20 #42B25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.14586

Abstract

For p>p₀=(2λ)/(2λ+1) with λ>0, the Hardy space H_λ^p(ℝ₊²) associated with the Dunkl transform F_λ and the Dunkl operator D on the real line ℝ, where D_xf(x)=f'(x)+\fracλx[f(x)-f(-x)], is the set of functions F=u+iv on the upper half plane ℝ²₊=\(x, y): x∈ℝ, y>0\, satisfying λ-Cauchy-Riemann equations: D_xu-∂_y v=0, ∂_y u +D_xv=0, and sup_y>0∫_ℝ|F(x+iy)|^p|x|^2λdx<∞ in [7]. Then it is proved in [11] that the real Dunkl-Hardy Spaces H_λ^p(ℝ) for (1)/(1+γ_λ)

Related

• The Real Characterization of H_λ^p(\mathbb R₊²) for (2λ)/(2λ+1)
• Hardy spaces associated with One-dimensional Dunkl transform for (2λ)/(2λ+1)
• Cesàro operator on Hardy spaces associated with the Dunkl setting ((2λ)/(2λ+1)
• Harmonic functions, conjugate harmonic functions and the Hardy space H¹ in the rational Dunkl setting
• Some results on the Hardy space H1 associated with the Dunkl operators