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arXiv · 1712.04321

Estimates for fractional integral operators and linear commutators on certain weighted amalgam spaces

Hua Wang
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Abstract

In this paper, we first introduce some new classes of weighted amalgam spaces. Then we give the weighted strong-type and weak-type estimates for fractional integral operators $I_\gamma$ on these new function spaces. Furthermore, the weighted strong-type estimate and endpoint estimate of linear commutators $[b,I_{\gamma}]$ generated by $b$ and $I_{\gamma}$ are established as well. In addition, we are going to study related problems about two-weight, weak type inequalities for $I_{\gamma}$ and $[b,I_{\gamma}]$ on the weighted amalgam spaces and give some results. Based on these results and pointwise domination, we can prove norm inequalities involving fractional maximal operator $M_{\gamma}$ and generalized fractional integrals $\mathcal L^{-\gamma/2}$ in the context of weighted amalgam spaces, where $0<\gamma<n$ and $\mathcal L$ is the infinitesimal generator of an analytic semigroup on $L^2(\mathbb R^n)$ with Gaussian kernel bounds.

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Hua Wang. 2017-11-19. Estimates for fractional integral operators and linear commutators on certain weighted amalgam spaces. https://arxiv.org/abs/1712.04321

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