L^p-Mapping Properties of a Class of Spherical Integral Operators

In this paper, we study a class of spherical integral operators (Formula presented.). We prove an inequality that relates this class of operators with some well-known Marcinkiewicz integral operators by using the classical Hardy inequality. We also attain the boundedness of the operator (Formula presented.) for some (Formula presented.) whenever (Formula presented.) belongs to a certain class of Lebesgue spaces. In addition, we introduce a new proof of the optimality condition on (Formula presented.) in order to obtain the (Formula presented.) -boundedness of (Formula presented.). Generally, the purpose of this work is to set up new proofs and extend several known results connected with a class of spherical integral operators.