• Communications of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.401-430
• /
• 2023

In this paper, we prove L^p estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in L(log L)² (𝕊^n-1 × 𝕊^m-1). Furthermore, we prove L^p estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.

• Kyungpook Mathematical Journal
• /
• v.63 no.4
• /
• pp.577-591
• /
• 2023

In this paper we establish the L^p boundedness of Marcinkiewicz integral operators on product domains with rough kernels satisfying a weak size condition. We assume that our kernels are supported on surfaces generated by curves more general than polynomials and convex functions. This generalizes and extends previous results.