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

In this paper, we study a class of spherical integral operators I Ω f . 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 I Ω f for some 1 < p < 2 whenever Ω belongs to a certain class of Lebesgue spaces. In addition, we introduce a new proof of the optimality condition on Ω in order to obtain the L 2 -boundedness of I Ω . 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. [ABSTRACT FROM AUTHOR]