Weighted weak-type inequalities for the maximal function of nonnegative integral transforms over approach regions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Weighted weak-type inequalities for the maximal function of nonnegative integral transforms over approach regions

Authors:	Shiying Zhao

Institution:	Department of Mathematics and Computer Science, University of Missouri-St. Louis, St. Louis, Missouri 63121

Abstract:	The relation between approach regions and singularities of nonnegative kernels is studied, where $t\in (0,\infty )$ , , $y\in X$ , and is a homogeneous space. For $1\le p<q<\infty$ , a sufficient condition on approach regions $\varOmega _a$ ( $a\in X$ ) is given so that the maximal function $\begin{equation}\sup _{(x,t)\in \Omg_{a}} \int _X K_t(x,y)f(y)\,d\sigma (y) \end{equation}$ is weak-type with respect to a pair of measures $\sigma$ and $\omega$ . It is shown that this condition is also necessary for operators of potential type in the sense of Sawyer and Wheedon (Amer. J. Math. 114 (1992), 813-874).

Keywords:	Weak type inequalities weights operators of potential type maximal functions approach regions

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