Axioms (Aug 2023)
<i>L<sup>p</sup></i>-Mapping Properties of a Class of Spherical Integral Operators
Abstract
In this paper, we study a class of spherical integral operators IΩf. 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 IΩf for some 1p2 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 L2-boundedness of IΩ. 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.
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