Corona and Wolff theorems for the multiplier algebra of Besov–Morrey spaces

Abstract

In this paper, we study the corona theorem and Wolff theorem for the multiplier algebra of the Besov–Morrey space ${\mathcal{B}}_p^{\lambda }(s)$ when $0<\lambda ,s<1<p<\mathrm{\infty }$. Here the Besov–Morrey space ${\mathcal{B}}_p^{\lambda }(s)$ is the space consisting of those analytic functions on the unit disc $\mathbb{D}$ such that $|f^{\prime }(z){|}^p(1-|z{|}^2{)}^{p+s-2}\mathrm{d}A(z)$ is a $\mathrm{\lambda s}$-Carleson measure.

Keywords:

• Besov–Morrey space
• Carleson measure
• corona theorem
• Wolff theorem

AMS Subject Classifications:

• 30H25
• 30H80

Acknowledgments

The authors would like to thank the referee for detailed comments that lead to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Foundation for Scientific and Technological Innovation in Department of Education of Guangdong Province [grant number 2021KTSCX182], Natural Science Foundation of Guangdong Province, China [grant number 2022A1515010317].