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arXiv · 1905.10946

Weighted estimates for bilinear fractional integral operators and their commutators on Morrey spaces

Qianjun He·Mingquan Wei·Dunyan Yan
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Abstract

This paper mainly dedicates to prove a plethora of weighted estimates on Morrey spaces for bilinear fractional integral operators and their general commutators with BMO functions of the form $$B_{\alpha}(f,g)(x)=\int_{\mathbb{R}^{n}}\frac{f(x-y)g(x+y)}{|y|^{n-\alpha}}dy,\qquad 0<\alpha<n.$$ We also prove some maximal function control theorems for these operators, that is, the weighted Morrey norm is bounded by the weighted Morrey norm of a natural maximal operator when the weight belongs to $A_{\infty}$. As a corollary, some new weighted estimates for the bilinear maximal function associated to the bilinear Hilbert transform are obtained. Furthermore, we formulate a bilinear version of Stein-Weiss inequality on Morrey spaces for fractional integrals.

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Qianjun He, Mingquan Wei, Dunyan Yan. 2019-05-27. Weighted estimates for bilinear fractional integral operators and their commutators on Morrey spaces. https://arxiv.org/abs/1905.10946

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