Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces

Junmei Wang

doi:doi:10.11648/j.pamj.20190801.13

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Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces

Junmei Wang

Published in Pure and Applied Mathematics Journal (Volume 8, Issue 1)

Received: 23 March 2019 Accepted: 22 April 2019 Published: 9 May 2019

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Abstract

In this paper, we study the boundedness of some sublinear operators with rough kernels, satisfied by most of the operators in classical harmonic analysis, on the generalized weighted grand Morrey spaces. More specifically, we show that the sublinear operators with rough kernels are bounded on these spaces under the conditions that the operators and the kernel functions satisfy some size conditions, and the operators are bounded on Lebesgue spaces. This is done by exploiting the well-known boundedness of sublinear operators with rough kernels on Lebesgue spaces, a more explicit decomposition of the generalized weighted grand Morrey spaces and the good properties of the weight functions and the kernel functions. Through combining some properties of A_p weight with the relevant lemmas of operators with rough kernel, we obtain the boundedness for sublinear operators with rough kernels on weighted grand morrey spaces. Furthermore, using the equivalent norm and the properties of BMO functions, an application of the boundedness of the sublinear operators with rough kernels to the corresponding commutators formed by certain operators and BMO functions are also considered. And the boundedness of commutator is obtained by the lemma of function BMO.

Published in	Pure and Applied Mathematics Journal (Volume 8, Issue 1)
DOI	10.11648/j.pamj.20190801.13
Page(s)	18-29
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

Keywords

Weighted Grand Morrey Space, Sublinear Operator, Rough Kernel, Commutator

References

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APA Style

Junmei Wang. (2019). Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces. Pure and Applied Mathematics Journal, 8(1), 18-29. https://doi.org/10.11648/j.pamj.20190801.13

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ACS Style

Junmei Wang. Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces. Pure Appl. Math. J. 2019, 8(1), 18-29. doi: 10.11648/j.pamj.20190801.13

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AMA Style

Junmei Wang. Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces. Pure Appl Math J. 2019;8(1):18-29. doi: 10.11648/j.pamj.20190801.13

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@article{10.11648/j.pamj.20190801.13,
  author = {Junmei Wang},
  title = {Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces},
  journal = {Pure and Applied Mathematics Journal},
  volume = {8},
  number = {1},
  pages = {18-29},
  doi = {10.11648/j.pamj.20190801.13},
  url = {https://doi.org/10.11648/j.pamj.20190801.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20190801.13},
  abstract = {In this paper, we study the boundedness of some sublinear operators with rough kernels, satisfied by most of the operators in classical harmonic analysis, on the generalized weighted grand Morrey spaces. More specifically, we show that the sublinear operators with rough kernels are bounded on these spaces under the conditions that the operators and the kernel functions satisfy some size conditions, and the operators are bounded on Lebesgue spaces. This is done by exploiting the well-known boundedness of sublinear operators with rough kernels on Lebesgue spaces, a more explicit decomposition of the generalized weighted grand Morrey spaces and the good properties of the weight functions and the kernel functions. Through combining some properties of Ap weight with the relevant lemmas of operators with rough kernel, we obtain the boundedness for sublinear operators with rough kernels on weighted grand morrey spaces. Furthermore, using the equivalent norm and the properties of BMO functions, an application of the boundedness of the sublinear operators with rough kernels to the corresponding commutators formed by certain operators and BMO functions are also considered. And the boundedness of commutator is obtained by the lemma of function BMO.},
 year = {2019}
}

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TY  - JOUR
T1  - Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces
AU  - Junmei Wang
Y1  - 2019/05/09
PY  - 2019
N1  - https://doi.org/10.11648/j.pamj.20190801.13
DO  - 10.11648/j.pamj.20190801.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 18
EP  - 29
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20190801.13
AB  - In this paper, we study the boundedness of some sublinear operators with rough kernels, satisfied by most of the operators in classical harmonic analysis, on the generalized weighted grand Morrey spaces. More specifically, we show that the sublinear operators with rough kernels are bounded on these spaces under the conditions that the operators and the kernel functions satisfy some size conditions, and the operators are bounded on Lebesgue spaces. This is done by exploiting the well-known boundedness of sublinear operators with rough kernels on Lebesgue spaces, a more explicit decomposition of the generalized weighted grand Morrey spaces and the good properties of the weight functions and the kernel functions. Through combining some properties of Ap weight with the relevant lemmas of operators with rough kernel, we obtain the boundedness for sublinear operators with rough kernels on weighted grand morrey spaces. Furthermore, using the equivalent norm and the properties of BMO functions, an application of the boundedness of the sublinear operators with rough kernels to the corresponding commutators formed by certain operators and BMO functions are also considered. And the boundedness of commutator is obtained by the lemma of function BMO.
VL  - 8
IS  - 1
ER  -

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Author Information

Junmei Wang

School of Mathematics and Statistics, Shandong Normal University, Jinan, China

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Plain Text BibTeX RIS

APA Style

Junmei Wang. (2019). Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces. Pure and Applied Mathematics Journal, 8(1), 18-29. https://doi.org/10.11648/j.pamj.20190801.13

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ACS Style

Junmei Wang. Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces. Pure Appl. Math. J. 2019, 8(1), 18-29. doi: 10.11648/j.pamj.20190801.13

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AMA Style

Junmei Wang. Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces. Pure Appl Math J. 2019;8(1):18-29. doi: 10.11648/j.pamj.20190801.13

Copy | Download

@article{10.11648/j.pamj.20190801.13,
  author = {Junmei Wang},
  title = {Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces},
  journal = {Pure and Applied Mathematics Journal},
  volume = {8},
  number = {1},
  pages = {18-29},
  doi = {10.11648/j.pamj.20190801.13},
  url = {https://doi.org/10.11648/j.pamj.20190801.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20190801.13},
  abstract = {In this paper, we study the boundedness of some sublinear operators with rough kernels, satisfied by most of the operators in classical harmonic analysis, on the generalized weighted grand Morrey spaces. More specifically, we show that the sublinear operators with rough kernels are bounded on these spaces under the conditions that the operators and the kernel functions satisfy some size conditions, and the operators are bounded on Lebesgue spaces. This is done by exploiting the well-known boundedness of sublinear operators with rough kernels on Lebesgue spaces, a more explicit decomposition of the generalized weighted grand Morrey spaces and the good properties of the weight functions and the kernel functions. Through combining some properties of Ap weight with the relevant lemmas of operators with rough kernel, we obtain the boundedness for sublinear operators with rough kernels on weighted grand morrey spaces. Furthermore, using the equivalent norm and the properties of BMO functions, an application of the boundedness of the sublinear operators with rough kernels to the corresponding commutators formed by certain operators and BMO functions are also considered. And the boundedness of commutator is obtained by the lemma of function BMO.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces
AU  - Junmei Wang
Y1  - 2019/05/09
PY  - 2019
N1  - https://doi.org/10.11648/j.pamj.20190801.13
DO  - 10.11648/j.pamj.20190801.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 18
EP  - 29
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20190801.13
AB  - In this paper, we study the boundedness of some sublinear operators with rough kernels, satisfied by most of the operators in classical harmonic analysis, on the generalized weighted grand Morrey spaces. More specifically, we show that the sublinear operators with rough kernels are bounded on these spaces under the conditions that the operators and the kernel functions satisfy some size conditions, and the operators are bounded on Lebesgue spaces. This is done by exploiting the well-known boundedness of sublinear operators with rough kernels on Lebesgue spaces, a more explicit decomposition of the generalized weighted grand Morrey spaces and the good properties of the weight functions and the kernel functions. Through combining some properties of Ap weight with the relevant lemmas of operators with rough kernel, we obtain the boundedness for sublinear operators with rough kernels on weighted grand morrey spaces. Furthermore, using the equivalent norm and the properties of BMO functions, an application of the boundedness of the sublinear operators with rough kernels to the corresponding commutators formed by certain operators and BMO functions are also considered. And the boundedness of commutator is obtained by the lemma of function BMO.
VL  - 8
IS  - 1
ER  -

Copy | Download