Shifted Hardy inequalities on the unit ball and polydisk
Year: 2026
Type: article
Abstract: We refine and extend shifted Hardy inequalities in several complex variables. A sharp estimate for homogeneous holomorphic polynomials on the sphere in Cn, combined with Yang's one-variable inequality and a slice identity, yields ball inequalities for H1(Bn), including a Bergman-scale family with weights. We also prove product inequalities on Dn and mixed-norm extensions for radial measures, where coefficient weights are moments of the measure. Motivated by Yang's shifted Hilbert form, we define a linear transform, derive its integral representation, compute its exact Hp(Bn)→Hp(Bn) norm, and obtain an H1(Bn)→H∞(Bn) bound.
Author: Adel Khalfallah
Institution: King Fahd University of Petroleum and Minerals
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204254499