Lacunary series in quaternion B^p,q spaces

Abstract

The main theme of this article is to obtain characterizations of B ^p,q -functions by the coefficients of certain lacunary series expansions in quaternionic sense. Moreover, we consider a scale of weighted spaces of quaternion-valued functions of three real variables. This scale generalizes the idea of Besov space in the complex function theory. Finally, we prove that the inclusions of spaces from the scale are strict inclusions.

Keywords:

• quaternion analysis
• B ^p,q spaces
• Hadamard gaps

AMS Subject Classifications:

• 46E15
• 30G35

Acknowledgements

The author would like to thank the referees for their valuable comments and interesting suggestions on this article.