Boundedness of some operators on weighted amalgam spaces

Abstract

Let $t\in (0,\infty )$, $p\in (1,\infty )$, $q\in [1,\infty ]$, $w\in A_p$ and $v\in A_q$. We introduce the weighted amalgam space $(L^p,L^q{)}_t({\mathbb{R}}^n)$ and show some properties of it. Some estimates on these spaces for the classical operators in harmonic analysis, such as the Hardy--Littlewood maximal operator, the Calderón--Zygmund operator, the Riesz potential, singular integral operators with the rough kernel, the Marcinkiewicz integral, the Bochner-Riesz operator, the Littlewood-Paley $g$ function and the intrinsic square function, are considered. Our main method is extrapolation. We obtain some new weak results for these operators on weighted amalgam spaces.