Unified Extrapolation Frameworks for Nonlinear, Weighted, Fractal, and Quantum Function Spaces

Abstract

We extend the classical Yano-Zygmund extrapolation theory by developing novel pointwise estimates and rearrangement inequalities for a broad class of operators and function spaces. In particular, we establish extrapolation results for nonlinear operators and adapt the theory to weighted and variable exponent spaces. Furthermore, we introduce extensions in the setting of noncommutative function spaces and analyze singular integral operators on fractal measures. Applications to harmonic analysis, partial differential equations, and quantum information theory are discussed.