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.
| Published in | Pure and Applied Mathematics Journal (Volume 8, Issue 3) |
| DOI | 10.11648/j.pamj.20190803.11 |
| Page(s) | 47-53 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2019. Published by Science Publishing Group |
Two Weight, Maximal Operator, Lebesgue Space
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APA Style
Hu Yunpeng, Cao Yonghui. (2019). Two Weight Characterization of New Maximal Operators. Pure and Applied Mathematics Journal, 8(3), 47-53. https://doi.org/10.11648/j.pamj.20190803.11
ACS Style
Hu Yunpeng; Cao Yonghui. Two Weight Characterization of New Maximal Operators. Pure Appl. Math. J. 2019, 8(3), 47-53. doi: 10.11648/j.pamj.20190803.11
AMA Style
Hu Yunpeng, Cao Yonghui. Two Weight Characterization of New Maximal Operators. Pure Appl Math J. 2019;8(3):47-53. doi: 10.11648/j.pamj.20190803.11
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Download@article{10.11648/j.pamj.20190803.11,
author = {Hu Yunpeng and Cao Yonghui},
title = {Two Weight Characterization of New Maximal Operators},
journal = {Pure and Applied Mathematics Journal},
volume = {8},
number = {3},
pages = {47-53},
doi = {10.11648/j.pamj.20190803.11},
url = {https://doi.org/10.11648/j.pamj.20190803.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20190803.11},
abstract = {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.},
year = {2019}
}
TY - JOUR T1 - Two Weight Characterization of New Maximal Operators AU - Hu Yunpeng AU - Cao Yonghui Y1 - 2019/08/05 PY - 2019 N1 - https://doi.org/10.11648/j.pamj.20190803.11 DO - 10.11648/j.pamj.20190803.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 47 EP - 53 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20190803.11 AB - 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. VL - 8 IS - 3 ER -
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