$L^{p}$ BOUNDS FOR MARCINKIEWICZ INTEGRALS

In this paper the authors establish the $L^p$ boundedness for several classes of Marcinkiewicz integral operators with kernels satisfying a condition introduced by Grafakos and Stefanov in Indiana Univ. Math. J.47 (1998), 455–469.AMS 2000 Mathematics subject classification: Primary 42B25; 42B99

A DIMENSION-DEPENDENT MAXIMAL INEQUALITY

In this short note we show that $\sup\{\|M_\nu\|:\nu\text{ is a measure on }\mathbb{R}^n\}$, where $\|M_\nu\|$ denotes the centred Hardy–Littlewood maximal operator, depends exponentially on $n$.AMS 2000 Mathematics subject classification: Primary 42B25