Weighted Calderón-Hardy spaces

2022/03/21 by Rocha, Pablo
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.10691

Abstract

Let 0 < p ≤ 1 < q < ∞ and γ>0. In this note we discuss the weighted Calderón-Hardy spaces on ℝⁿ, H^p_{q, γ}(ℝⁿ, w). For γ= 2m, m ∈ ℕ, and n (2m + n/q)^-1 < p ≤ 1, we show that for certain power weights w the iterated Laplace operator Δ^m is a bijective mapping from H^p_{q, 2m}(ℝⁿ,w) onto H^p(ℝⁿ, w).

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