Revisiting Taibleson's theorem

Humberto Rafeiro; Joel E. Restrepo; Humberto Rafeiro; Joel E. Restrepo

doi:10.3934/era.2022029

Electronic Research Archive

2022, Volume 30, Issue 2: 565-573. doi: 10.3934/era.2022029

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Revisiting Taibleson's theorem

Humberto Rafeiro ¹,
Joel E. Restrepo ^{2
,
,}

1.
Department of Mathematical Sciences, United Arab Emirates University, UAE
2.
Department of Mathematics, Nazarbayev University, Kazakhstan & Regional Mathematical Center, Southern Federal University, Russia

Received: 26 November 2021 Revised: 25 January 2022 Accepted: 26 January 2022 Published: 10 February 2022

A new characterization of the weighted Taibleson's theorem for generalized Hölder spaces is given via a Hadamard-Liouville type operator (Djrbashian's generalized fractional operator).
- generalized Hölder space,
- Bari-Stechkin class,
- modulus of continuity,
- generalized fractional operator,
- harmonic function,
- poisson integral
Citation: Humberto Rafeiro, Joel E. Restrepo. Revisiting Taibleson's theorem[J]. Electronic Research Archive, 2022, 30(2): 565-573. doi: 10.3934/era.2022029

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Abstract

A new characterization of the weighted Taibleson's theorem for generalized Hölder spaces is given via a Hadamard-Liouville type operator (Djrbashian's generalized fractional operator).

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