An elementary proof of a Riesz-Thorin type Theorem

Abstract: A well known theorem of Riesz and Thorin states that an operator that is bounded on the Lebesgue spaces of exponent $p=1$ and $p=\infty$ is automatically bounded on the intermediate spaces of exponent $1 \leq p \leq \infty$. In 1980 Peter Jones gave a proof of the analogous result for the analytic Hardy spaces $H^{p}$ based on explicit solutions for the $\overline{\partial}$-problem in the upper half-plane. In this talk we will give a new elementary proof of this result. The ideas are inspired by recent work on factorization in spaces of analytic functions with a complete Nevanlinna-Pick kernel.

This talk is based on joint work with Alexandru Aleman.

Contact Antti Perälä to receive the Zoom link.