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. Copyright © 2018 Informa UK Limited, trading as Taylor & Francis Group.
CitationHo, K.-P. (2018). The Ahlfors-Beurling transform on Morrey spaces with variable exponents. Integral Transforms and Special Functions, 29(3), 207-220. doi: 10.1080/10652469.2017.1422498
- Ahlfors–Beurling transform
- Morrey space
- Lebesgue space
- Variable exponent