Data: 4 listopada 2025 (wtorek), godzina 11:00-12:00, sala A1-33
Miejsce: Aula A
Prelegent: Professor Enrique A. Sànchez Pèrez (IUMPA-Universitat Politècnica de València)
Streszczenie: A core objective in functional analysis is the extension of operators to broader spaces while preserving key properties. Starting with a given vector measure, \(m\), we define the subspace \(\mathbf{V_p(m)} \subset L^1(m)\), which consists of functions whose induced scalar measure has finite \(p\)-variation. The foundational result we present shows that \(V_p(m)\) is maximal for ensuring the preservation of lower \(p\)-estimates. Vector measure representations offer a flexible and robust framework for extending operators defined on various Banach function spaces. Depending on the specific properties intended for preservation, this technique identifies the largest possible subspaces on which these operator extensions continue to satisfy the required property. In this talk, we will focus our attention specifically on lower \(p\)-estimates and their critical role for both the \(\mathbf{V_p(m)}\) spaces and the operators defined upon them.