Hardy-Littlewood, Bessel-Riesz, and Fractional Integral Operators in Anisotropic Morrey and Campanato Spaces

Abstract

This paper investigates the boundedness of key harmonic analysis operators—including the Hardy‑Littlewood maximal operator, Bessel‑Riesz operators, generalized Bessel‑Riesz operators, and generalized fractional integral operators—in generalized local (central) Morrey spaces and Campanato spaces over homogeneous (anisotropic) Lie groups. It also establishes Olsen‑type inequalities and extends classical Euclidean results to a more general anisotropic and homogeneous group setting, allowing arbitrary homogeneous quasi‑norms.