ABSTRACT
We establish the vector-valued inequalities of the Ahlfors–Beurling operator on Morrey spaces with variable exponents. As consequences of these inequalities, we have the boundedness of the Ahlfors–Beurling transform on Lebesgue spaces with variable exponents and Morrey spaces. The results obtained in this paper are new in the case of Morrey spaces.
Acknowledgements
The author would like to thank the reviewers for their valuable comments and suggestions, especially, on the proof of Theorem 4.5.
Disclosure statement
No potential conflict of interest was reported by the author.