Bounds for a class of two-dimensional integrals involving mixed power-type singularities

Abstract

This article investigates two-dimensional integrals involving singularities and multiplicative compositions. The main focus is on deriving lower and upper bounds under various assumptions on the primary function, including monotonicity, convexity, and sub-multiplicativity. The results are presented with complete proofs and are intended to motivate further developments in the study of integral inequalities.