在本文中，我们考虑双线性算子$\mathrm{<trans\; data-src="T">T型</trans>}$满足存在正常数${\mathrm{<trans\; data-src="C">C类</trans>}}_{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="T">T型</trans>}<trans\; data-src=")">)</trans>}$，取决于$\mathrm{<trans\; data-src="T">T型</trans>}$这样，对于任何可测量的函数$\mathrm{<trans\; data-src="f">（f）</trans>}$和$\mathrm{<trans\; data-src="g">克</trans>}$具有紧凑的支撑，$\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans>\mathrm{<trans\; data-src="ℝ">ℝ</trans>}$具有、和$\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="ℝ">ℝ</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}}$具有$\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="\notin ">\notin </trans>\text{<trans data-src="supp">支持</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="f">（f）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\cdot ">\cdot </trans><trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="\cap ">\cap </trans>\text{<trans data-src="supp">支持</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="g">克</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="-">-</trans><trans\; data-src="\cdot ">\cdot </trans><trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>$,

$$\left|\mathrm{<trans\; data-src="T">T型</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="f">（f）</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="g">克</trans>}<trans\; data-src=")">)</trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src=")">)</trans>\right|<trans\; data-src="\le ">\le </trans>{\mathrm{<trans\; data-src="C">C类</trans>}}_{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="T">T型</trans>}<trans\; data-src=")">)</trans>}{\displaystyle {<trans\; data-src="\int ">\int </trans>}_{{\mathrm{<trans\; data-src="ℝ">ℝ</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}}}\frac{\left|\mathrm{<trans\; data-src="f">（f）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="t">t吨</trans>}\mathrm{<trans\; data-src="y">年</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="g">克</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="y">年</trans>}<trans\; data-src=")">)</trans>\right|}{<trans\; data-src="|">|</trans>\mathrm{<trans\; data-src="y">年</trans>}{<trans\; data-src="|">|</trans>}^{\mathrm{<trans\; data-src="n">n个</trans>}}}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="y">年</trans>}}<trans\; data-src=".">.</trans>$$

我们研究了$\mathrm{<trans\; data-src="T">T型</trans>}$关于消失的广义Morrey空间${\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}{\mathrm{<trans\; data-src="L">L（左）</trans>}}^{\mathrm{<trans\; data-src="p">第页</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="ℝ">ℝ</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}}<trans\; data-src=")">)</trans>$和${\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="\infty ">\infty </trans>}}{\mathrm{<trans\; data-src="L">L（左）</trans>}}^{\mathrm{<trans\; data-src="p">第页</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="ℝ">ℝ</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}}<trans\; data-src=")">)</trans>$，以及次双线性极大算子的有界性$\mathcal{<trans\; data-src="ℳ">ℳ</trans>}$关于消失的广义Morrey空间${\mathrm{<trans\; data-src="V">V（V）</trans>}}^{<trans\; data-src="(">(</trans><trans\; data-src="\ast ">\ast </trans><trans\; data-src=")">)</trans>}{\mathrm{<trans\; data-src="L">L（左）</trans>}}^{\mathrm{<trans\; data-src="p">第页</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="ℝ">ℝ</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}}<trans\; data-src=")">)</trans>$，及其在谐波分析中对一些经典（次）双线性算子的应用。作为副产品，我们还表明$\mathrm{<trans\; data-src="T">T型</trans>}$在广义Morrey空间上有界${\mathrm{<trans\; data-src="L">L（左）</trans>}}^{\mathrm{<trans\; data-src="p">第页</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="ℝ">ℝ</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}}<trans\; data-src=")">)</trans>$本文的主要结果还包括一些典型的例子。