Lp Bounds for Rough Maximal Operators along Surfaces of Revolution on Product Domains - Mohammed Ali; Hussain Al-Qassem (Mathematics, 2024)
In this paper, we study the boundedness of rough Maximal integral operators along surfaces of revolution on product domains. For several classes of surfaces, we establish appropriate <semantics>Lp</semantics> bounds of these Maximal operators under the assumption <semantics>Ω∈Lq(Sm−1×Sn−1)</semantics> for some <semantics>q>1</semantics>, and then we employ these bounds along with Yano’s extrapolation argument to obtain the <semantics>Lp</semantics> boundedness of the aforementioned integral operators under a weaker condition in which <semantics>Ω</semantics> belongs to either the space <semantics><msubsup>Bq(0,2τ′−1)</msubsup>(Sm−1×Sn−1)</semantics> or to the space <semantics>L(logL)2/τ′(Sm−×Sn−1)</semantics>. Our results extend and improve many previously known results.