Fractional integral and maximal operators in measure space settings. Link inequalities

Motivated by results in Euclidean harmonic analysis related to Riesz potential and Hardy-Littlewood maximal operators, the article investigates fractional integral and maximal operators associated with measurable kernels in general measure space settings. The goal is to characterize kernels that yield link inequalities for such operators, and to determine their sharp forms. Applications include generalizations to higher dimension of results in single variable complex analysis and quantitative Hartogs-Rosenthal theorems for elliptic differential operators.