On slice regular fractal-fractional Dirichlet type spaces

2025/06/17 by José Óscar González-Cervantes, González-Cervantes, José Oscar, Carlos Alejandro Moreno‐Muñoz +3
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2506.14172

openalex publication_date 2025/06/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

In this paper, we study some families of right modules of quaternionic slice regular functions induced by a generalized fractal-fractional derivative with respect to a truncated quaternionic exponential function on slices. Important Banach spaces of slice regular functions, namely the Bergman and the Dirichlet modules, are two important elements of one of our families.

Citations

• Fractional slice regular functions of a quaternionic variable
• BMO- and VMO-spaces of slice hyperholomorphic functions
• Entire slice regular functions
• Further properties of the Bergman spaces of slice regular functions
• Bloch, Besov and Dirichlet spaces of slice hyperholomorphic functions

Related

• Fractional slice regular functions of a quaternionic variable
• Some slice regular functions in several variables and fiber bundles
• On some quaternionic generalized slice regular functions
• On fiber bundles and quaternionic slice regular functions
• On slice regular Bergman spaces and fiber bundles