Estimates for Riesz potential on weighted variable Hardy spaces revisited

2025/11/02 by Rocha, Pablo
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.01102

Abstract

In [Math. Ineq. & appl., Vol 26 (2) (2023), 511-530] and [Period. Math. Hung., 89 (1) (2024), 116-128], the present author proved that the Riesz potential I_α extends to a bounded operator H^p(⋅)_ω(ℝⁿ) → L^q(⋅)_ω(ℝⁿ) and H^p(⋅)_ω(ℝⁿ) → H^q(⋅)_ω(ℝⁿ) respectively, under the following two assumptions: A1) ω∈ W_q(⋅) with q(⋅) ∈ P^log(ℝⁿ) and (1)/(p(⋅)) := (1)/(q(⋅)) + \fracαn; A2) for every cube Q ⊂ ℝⁿ, ‖ χ_Q ‖_L^q(⋅)ω ≈ |Q|^-α/n ‖ χ_Q ‖_L^p(⋅)ω. In this note, we re-establish such estimates for I_α without assuming the hypothesis A2). These proofs are simpler than the previous ones.

Citations

• Inequalities for weighted spaces with variable exponents
• A new approach to norm inequalities on weighted and variable Hardy\n spaces
• On the atomic and molecular decomposition of weighted Hardy spaces
• Boundedness of generalized Riesz potentials on the variable Hardy spaces
• Fractional type integral operators on variable Hardy spaces
• Hardy spaces with variable exponents and generalized Campanato spaces
• Multilinear Calderón-Zygmund operators on Hardy spaces

Related

• Weighted estimates for generalized Riesz potentials
• Boundedness of generalized Riesz potentials on the variable Hardy spaces
• A note about discrete Riesz potential on ℤⁿ
• Inequalities for weighted spaces with variable exponents
• The H^p(ℤⁿ)-H^q(ℤⁿ) boundedness of the discrete Riesz potential