Boundedness of Littlewood-Paley Operators in Variable Morrey Spaces

Panwang Wang; Zongguang Liu

doi:doi:10.11648/j.ajam.20221002.11

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Boundedness of Littlewood-Paley Operators in Variable Morrey Spaces

Panwang Wang, Zongguang Liu

Published in American Journal of Applied Mathematics (Volume 10, Issue 2)

Received: 14 February 2022 Accepted: 7 March 2022 Published: 17 March 2022

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Abstract

In this paper, the authors prove norm inequalities for the intrinsic square functions and commutators generated by this class operator and BMO function in variable Morrey spaces. This implies that the same norm inequalities for the Lusin area integrals, the Littlewood-Paley operators and the continuous square functions. As application, we get the boundedness for convolution Calderón-Zygmund operators in generalized Morrey spaces.

Published in	American Journal of Applied Mathematics (Volume 10, Issue 2)
DOI	10.11648/j.ajam.20221002.11
Page(s)	15-28
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), 2024. Published by Science Publishing Group

Keywords

Littlewood-Paley Operators, Singular Integrals, Morrey Spaces, Commutator

References

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APA Style

Panwang Wang, Zongguang Liu. (2022). Boundedness of Littlewood-Paley Operators in Variable Morrey Spaces. American Journal of Applied Mathematics, 10(2), 15-28. https://doi.org/10.11648/j.ajam.20221002.11

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ACS Style

Panwang Wang; Zongguang Liu. Boundedness of Littlewood-Paley Operators in Variable Morrey Spaces. Am. J. Appl. Math. 2022, 10(2), 15-28. doi: 10.11648/j.ajam.20221002.11

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AMA Style

Panwang Wang, Zongguang Liu. Boundedness of Littlewood-Paley Operators in Variable Morrey Spaces. Am J Appl Math. 2022;10(2):15-28. doi: 10.11648/j.ajam.20221002.11

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@article{10.11648/j.ajam.20221002.11,
  author = {Panwang Wang and Zongguang Liu},
  title = {Boundedness of Littlewood-Paley Operators in Variable Morrey Spaces},
  journal = {American Journal of Applied Mathematics},
  volume = {10},
  number = {2},
  pages = {15-28},
  doi = {10.11648/j.ajam.20221002.11},
  url = {https://doi.org/10.11648/j.ajam.20221002.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20221002.11},
  abstract = {In this paper, the authors prove norm inequalities for the intrinsic square functions and commutators generated by this class operator and BMO function in variable Morrey spaces. This implies that the same norm inequalities for the Lusin area integrals, the Littlewood-Paley operators and the continuous square functions. As application, we get the boundedness for convolution Calderón-Zygmund operators in generalized Morrey spaces.},
 year = {2022}
}

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TY  - JOUR
T1  - Boundedness of Littlewood-Paley Operators in Variable Morrey Spaces
AU  - Panwang Wang
AU  - Zongguang Liu
Y1  - 2022/03/17
PY  - 2022
N1  - https://doi.org/10.11648/j.ajam.20221002.11
DO  - 10.11648/j.ajam.20221002.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 15
EP  - 28
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20221002.11
AB  - In this paper, the authors prove norm inequalities for the intrinsic square functions and commutators generated by this class operator and BMO function in variable Morrey spaces. This implies that the same norm inequalities for the Lusin area integrals, the Littlewood-Paley operators and the continuous square functions. As application, we get the boundedness for convolution Calderón-Zygmund operators in generalized Morrey spaces.
VL  - 10
IS  - 2
ER  -

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Author Information

Panwang Wang

Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, P. R. China
Zongguang Liu

Department of Mathematics, China University of Mining and Technology, Beijing, P. R. China

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APA Style

Panwang Wang, Zongguang Liu. (2022). Boundedness of Littlewood-Paley Operators in Variable Morrey Spaces. American Journal of Applied Mathematics, 10(2), 15-28. https://doi.org/10.11648/j.ajam.20221002.11

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ACS Style

Panwang Wang; Zongguang Liu. Boundedness of Littlewood-Paley Operators in Variable Morrey Spaces. Am. J. Appl. Math. 2022, 10(2), 15-28. doi: 10.11648/j.ajam.20221002.11

Copy | Download

AMA Style

Panwang Wang, Zongguang Liu. Boundedness of Littlewood-Paley Operators in Variable Morrey Spaces. Am J Appl Math. 2022;10(2):15-28. doi: 10.11648/j.ajam.20221002.11

Copy | Download

@article{10.11648/j.ajam.20221002.11,
  author = {Panwang Wang and Zongguang Liu},
  title = {Boundedness of Littlewood-Paley Operators in Variable Morrey Spaces},
  journal = {American Journal of Applied Mathematics},
  volume = {10},
  number = {2},
  pages = {15-28},
  doi = {10.11648/j.ajam.20221002.11},
  url = {https://doi.org/10.11648/j.ajam.20221002.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20221002.11},
  abstract = {In this paper, the authors prove norm inequalities for the intrinsic square functions and commutators generated by this class operator and BMO function in variable Morrey spaces. This implies that the same norm inequalities for the Lusin area integrals, the Littlewood-Paley operators and the continuous square functions. As application, we get the boundedness for convolution Calderón-Zygmund operators in generalized Morrey spaces.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Boundedness of Littlewood-Paley Operators in Variable Morrey Spaces
AU  - Panwang Wang
AU  - Zongguang Liu
Y1  - 2022/03/17
PY  - 2022
N1  - https://doi.org/10.11648/j.ajam.20221002.11
DO  - 10.11648/j.ajam.20221002.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 15
EP  - 28
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20221002.11
AB  - In this paper, the authors prove norm inequalities for the intrinsic square functions and commutators generated by this class operator and BMO function in variable Morrey spaces. This implies that the same norm inequalities for the Lusin area integrals, the Littlewood-Paley operators and the continuous square functions. As application, we get the boundedness for convolution Calderón-Zygmund operators in generalized Morrey spaces.
VL  - 10
IS  - 2
ER  -

Copy | Download