A molecular reconstruction theorem for H^p(⋅)_ω(ℝⁿ)

2022/11/26 by Rocha, Pablo
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.14606

Abstract

In this article we give a molecular reconstruction theorem for H_ω^p(⋅)(ℝⁿ). As an application of this result and the atomic decomposition developed in [5] we show that classical singular integrals can be extended to bounded operators on H_ω^p(⋅)(ℝⁿ). We also prove, for certain exponents q(⋅) and certain weights ω, that Riesz potential I_α, with 0 < α< n, can be extended to a bounded operator from H^p(⋅)_ω(ℝⁿ) into H^q(⋅)_ω(ℝⁿ), for (1)/(p(⋅)) := (1)/(q(⋅)) + \fracαn.

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