A Generalized Three Lines Lemma in Hardy-like Spaces
Abstract
Abstract In this paper we address the following question: given a holomorphic function with prescribed $$L^p(\mathbb {R})$$ L p ( R ) and $$L^q(\mathbb {R})$$ L q ( R ) norm (with $$1\le p,q \le \infty $$ 1 ≤ p , q ≤ ∞ ) along two parallel lines in the complex plane, what is the largest value that the function can attain at a prescribed point between these lines? Here we show that this problem is well-posed in suitable Hardy-like spaces on the strip. Moreover, in this setting we completely solve this problem by providing not only an explicit formula for the optimizers but also for the optimal values. In addition, we briefly discuss some applications of these results to interpolation theory and to Lieb-Thirring inequalities.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Finite Group Theory Research
Advanced Banach Space Theory
Publication details
- Journal / source
- Complex Analysis and Operator Theory
- Publisher
- Springer Science and Business Media LLC
- Volume
- 20
- Issue
- 6
- Publication date
- 16 July 2026
- Language
- EN