Changmei Tan

Integral Inequalities For Littlewood--Paley Operators

Abstract:
Let Tf denote the g-function g(f) or the area integral s(f). We give a characterization of functions $\Phi$ for which
$$ \Phi(\lambda)\big|\big\{x\in R^n:\;|Tf(x)|>\lambda\big\}\big|\leq C \int_{R^n} \Phi(|f(x)|)\,dx,$$
$$\int_{R^n} \Phi(|Tf(x)|)\,dx \leq C \int_{R^n} \Phi(|f(x)|)\,dx, $$
where the constant C is independent of f.

Keywords:
Littlewood-Paley g-function, area function, Orlicz space.

MSC 2000: 42B25