Boundedness of some operators on weighted amalgam spaces

2021/10/04 by Lu, Yuan, Wang, Songbai, Zhou, Jiang
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2110.01193

Abstract

Let t∈(0,∞), p∈(1,∞), q∈[1,∞], w∈ A_p and v∈ A_q. We introduce the weighted amalgam space (L^p,L^q)_t(\mathbb Rⁿ) 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.

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