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General weighted class of quaternion-valued functions with lacunary series expansions

Abstract

The purpose of this article is to define a new general weighted class of hyperholomorphic functions, the so called \({\mathbf {B}}^{q}_{\alpha ,\omega }(G)\) Spaces. For this class we obtain characterizations by weighted Bloch \({{\mathcal {B}}}^{\alpha }_{\omega }\) spaces. Moreover, we characterize the hyperholomorphic \({\mathbf {B}}^{q}_{\alpha ,\omega }(G)\) functions by the coefficients of certain lacunary series expansions in Clifford analysis.

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Acknowledgements

We would like to express our gratitude to the anonymous referees for their helpful suggestions and corrections.The authors declare that they have no competing interests.

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Correspondence to Alaa Kamal.

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Kamal, A., Yassen, T.I. General weighted class of quaternion-valued functions with lacunary series expansions. Afr. Mat. 33, 69 (2022). https://doi.org/10.1007/s13370-022-01004-w

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Keywords

  • Quaternionic analysis
  • \({\mathbf {B}}^{q}_{\alpha , \omega }(G)\) spaces
  • Hyperholomorphic functions
  • Clifford analysis

Mathematics Subject Classification

  • 32Axx
  • 32Hxx