O'Neil-type inequalities in Morrey spaces on the set T^n

Abstract: This paper studies O'Neil-type convolution inequalities in local and generalized Morrey spaces on the n-dimensional torus. We extend classical Minkowski and Young inequalities to the Morrey setting and obtain boundedness results for convolution operators. The main result is a generalization of O'Neil's inequality from Lorentz spaces to Morrey-type spaces via dyadic decompositions. We derive norm estimates for convolution operators between Morrey spaces with different parameters and characterize the admissible range of exponents ensuring boundedness. The proof relies on interpolation theory for Morrey spaces, Köthe duality, and real interpolation methods. We also establish embedding relations between local and generalized Morrey spaces. These results extend classical convolution inequalities and unify Lorentz and Morrey frameworks, with applications to partial differential equations and harmonic analysis.