Two-weighted conditions and characterizations for a class of multilinear fractional new maximal operators
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In this paper, two weight conditions are introduced and the multiple weighted strong and weak characterizations of the multilinear fractional new maximal operator $\mathcal{M}_{\varphi,\beta}$ are established. Meanwhile, we introduce the $S_{(\vec{p},q),\beta}(\varphi)$ and $B_{(\vec{p},q),\beta}(\varphi)$ conditions and obtain the characterization of two-weighted inequalities for $\mathcal{M}_{\varphi,\beta}$. Finally, the relationships of the conditions $S_{(\vec{p},q),\beta}(\varphi)$, $\mathcal{A}_{(\vec{p},q),\beta}(\varphi)$ and $B_{(\vec{p},q),\beta}(\varphi)$ and the characterization of the one-weight $A_{(\vec{p},q),\beta}(\varphi)$ are given.
Abstract
In this paper, two weight conditions are introduced and the multiple weighted strong and weak characterizations of the multilinear fractional new maximal operator $\mathcal{M}_{\varphi,\beta}$ are established. Meanwhile, we introduce the $S_{(\vec{p},q),\beta}(\varphi)$ and $B_{(\vec{p},q),\beta}(\varphi)$ conditions and obtain the characterization of two-weighted inequalities for $\mathcal{M}_{\varphi,\beta}$. Finally, the relationships of the conditions $S_{(\vec{p},q),\beta}(\varphi)$, $\mathcal{A}_{(\vec{p},q),\beta}(\varphi)$ and $B_{(\vec{p},q),\beta}(\varphi)$ and the characterization of the one-weight $A_{(\vec{p},q),\beta}(\varphi)$ are given.
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