A Note on Parabolic Maximal Operators along Surfaces of Revolution via Extrapolation

Abstract

Under weak conditions on the kernels, we obtain sharp Lp bounds for rough parabolic maximal integral operators over surfaces of revolution. By virtue of these bounds along with Yano’s extrapolation argument, we confirm the Lp boundedness of these maximal operators under weaker conditions on the kernels. Our obtained results represent substantial extensions and improvements of some known results on maximal operators with rough kernels on symmetric spaces.

A Note on a Class of Generalized Parabolic Marcinkiewicz Integrals along Surfaces of Revolution

“…The following two lemmas play a great role in the proofs of Theorems 1 and 2. They can be established by following the exact procedure utilized in [31] (with a very simple minor modification).…”