Convolution operators and variable Hardy spaces on the Heisenberg group

2024/03/18 by Pablo Rocha, Rocha, Pablo · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2403.11467

openalex publication_date 2024/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ℍⁿ be the Heisenberg group. For 0 ≤ α< Q=2n+2 and N ∈ ℕ we consider exponent functions p(⋅) : ℍⁿ → (0, +∞), which satisfies Hölder conditions, such that (Q)/(Q+N) < p_- ≤ p(⋅) ≤ p₊ < \fracQα. In this article we prove the H^p(⋅)(ℍⁿ) → L^q(⋅)(ℍⁿ) and H^p(⋅)(ℍⁿ) → H^q(⋅)(ℍⁿ) boundedness of convolution operators with kernels of type (α, N) on ℍⁿ, where (1)/(q(⋅)) = (1)/(p(⋅)) - \fracαQ. In particular, the Riesz potential on ℍⁿ satisfies such estimates.

Cited by

• A remark about Calderón-Hardy spaces with variable exponents
• Variable Calderón-Hardy spaces on the Heisenberg group

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