Boundedness of the Gaussian Riesz Potentials on Gaussian variable Lebesgue spaces

2022/08/25 by Eduard Navas, Navas, Eduard, Ebner Pineda +3
Mathematics · #42B35 #47G10 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 42B25 #Secondary 46E30

paper · pdf · doi:10.48550/arxiv.2208.11864

openalex publication_date 2022/08/25 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28

Abstract

In this paper we prove the boundedness of the Gaussian Riesz potentials I_β, for β≥ 1 on L^p(⋅)(γ_d), the Gaussian variable Lebesgue spaces under a certain additional condition of regularity on p(⋅) following \citeDalSco. Additionally, this result trivially gives us an alternative proof of the boundedness of Gaussian Riesz potentials I_β on Gaussian Lebesgue spaces L^p(γ_d).

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