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arXiv · 2110.01193

Boundedness of some operators on weighted amalgam spaces

Yuan Lu·Songbai Wang·Jiang Zhou
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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 Calder\'on--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.

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Yuan Lu, Songbai Wang, Jiang Zhou. 2021-10-04. Boundedness of some operators on weighted amalgam spaces. https://arxiv.org/abs/2110.01193

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