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Volume 8, Issue 3, June 2019, Page: 47-53
Two Weight Characterization of New Maximal Operators
Hu Yunpeng, Department of Mathematics and Systems Sciences, Xinjiang University, Urumqi, China
Cao Yonghui, Department of Mathematics and Systems Sciences, Xinjiang University, Urumqi, China
Received: Jun. 23, 2019;       Accepted: Jul. 19, 2019;       Published: Aug. 5, 2019
DOI: 10.11648/j.pamj.20190803.11      View  688      Downloads  158
For the last twenty years, there has been a great deal of interest in the theory of two weight. In the present paper, we investigate the two weight norm inequalities for fractional new maximal operator on the Lebesgue space. More specifically, we obtain that the sufficient and necessary conditions for strong and weak type two weight norm inequalities for a new fractional maximal operators by introducing a class of new two weight functions. In the discussion of strong type two weight norm inequalities, we make full use of the properties of dyadic cubes and truncation operators, and utilize the space decomposition technique which space is decomposed into disjoint unions. In contrast, weak type two weight norm inequalities are more complex. We have the aid of some good properties of Ap weight functions and ingeniously use the characteristic function. What should be stressed is that the new two weight functions we introduced contains the classical two weights and our results generalize known results before. In this paper, it is worth noting that w(x)dx may not be a doubling measure if our new weight functions ω∈Ap (φ). Since φ(|Q|)≥1, our new weight functions are including the classical Muckenhoupt weights.
Two Weight, Maximal Operator, Lebesgue Space
To cite this article
Hu Yunpeng, Cao Yonghui, Two Weight Characterization of New Maximal Operators, Pure and Applied Mathematics Journal. Vol. 8, No. 3, 2019, pp. 47-53. doi: 10.11648/j.pamj.20190803.11
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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