Some Characterization of the Function Space Type of Lizorkin−Triebel−Morrey

Rena Eldar Kizi Kerbalayeva

doi:doi:10.11648/j.mcs.20210604.11

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Some Characterization of the Function Space Type of Lizorkin−Triebel−Morrey

Rena Eldar Kizi Kerbalayeva

Published in Mathematics and Computer Science (Volume 6, Issue 4)

Received: 29 May 2021 Accepted: 8 June 2021 Published: 30 August 2021

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Abstract

This paper will introduce you to some properties of normed function spaces with many groups variables field of Analysis and it helps me appreciate how normed Lebesgue–Morrey space with many groups of variables that build and studied new normed spaces nowadays. Many of the topics here are important to an Analysis class. By reading this paper, you will discover the “embedding theory” of normed spaces type of Lebesgue–Morrey by introducing few of its “new functions with groups with variables” and along the way you will see to some interesting and article elements of the branch called Analysis. A lot of problems belonging to the characterization of various spaces of differentiability function spaces and relationships between them have been solved using the theory embedding theorems. The purpose of this paper is to review several embedding inequalities of normed spaces that will arise properties of these spaces and again throughout this material. We also give “working definition, notations” of a functions and function spaces. We must note that, the analysis is based on such function spaces to build new space type of Lizorkin–Triebel–Morrey. In addition, throughout this paper we will introduce a working normed function spaces type of Lizorkin–Triebel–Morrey with standard mathematical definitions and terminology. One aspect of this paper involves normed Lebesgue–Morey type spaces that can convert space from one to another.

Published in	Mathematics and Computer Science (Volume 6, Issue 4)
DOI	10.11648/j.mcs.20210604.11
Page(s)	59-64
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

The Space Type of Lesgue–Triebel−Morrey, Function Space of Differentiability Function, Many Groups of Variablesç

References

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[2]	Djabrailov A. Dj., Maksudov F. Q. (2000) The method integral representation in the theory of spaces. Baku, 3-190.
[3]	Guliyev V. S., Najafov A. M. (2001) The imbedding theorems on the Lizorkin−Triebel−Morrey type space.3rd International ISAAC Congren. Freie Universitat Berlin, Germany, august, 23−30.
[4]	Fan Di., Lu S., Yang D. (1998) Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients. Georgian Math. Jour., 5, 425–440.
[5]	Guiseppe, S. (1998) Un problema di Darboux in un insieme non limitato. Esistenza, unicita e dipendenza continua della soluzione. Math., 53 (2), 359−373.
[6]	Leyla Sh. Kadimova., Kerbalayeva R. E. (2019) On smothness of solution for the higher-order partial equations. Transactions Nat. Acade. Sci. Azerbaijan. Ser. Phys.-Tech. Math. Sci. Mathe., 39 (1), page 83–97.
[7]	Kerbalayeva R. E. (2021) Some characterization of the function space type of Lebesgue−Morrey. American Journal of İnformation Science and Technology, 5/12, 25-29.
[8]	Kokilashvili V., Samko S. (2003) Singular integrals in weighted Lebesgue spaces with variable exponent. Geor. Math. J., 10 (1), 145–156.
[9]	Kozano H. (1994) Comm. Partial Differential Navier−Stokes equations. Yamasaki M. Semilinear heat equations and the Navier−Stokes equation with distributions in new function spaces as initial data, 19, 959-1014.
[10]	Lin Tang., Jingshi Xu. (2005) Some properties of Morrey type Besov−Triebel spaces. Math. Nachr., 278 (7/8), 904−917.
[11]	Mazzucato, A. I. (2001) Decomposition of Besov−Morrey spaces. Proceedings of Conference on Harmonic Analysis, 215−233.
[12]	Najafov, A. M. (2005) On some properties of the function from Sobolev−Morrey type spaces. Central Europen Journal of Mathem., 3 (3), 496−507.
[13]	Najafov A. M. (2005) Some properties of functions from the intersection of Besov−Morrey type spaces with dominant mixed derivatives. Proceedings of A. Razmadze Math. Inst., 139, 71−82.
[14]	Najafov A. M. (2005) Problem on smoothness of solution of one class hypoelliptic equations. Proceedings of A. Razmadze Math. Inst., 140, 131−139.
[15]	Najafov A. M., Kerbalayeva R. E. (2015) Interpolation theorems for spaces Besov–Morrey type. Journal presented by institute Mathematics and Computer Sciences at Tskhum–Abkhazian Academy of Sciences, Tskhum–Abkhazian, IX–X, 198–212.
[16]	Najafov A. M., Kerbalayeva R. E. (2016) Some characterization of functions from Lizorkin–Triebel–Morrey type spaces with many groups variable. Transacions of NAS of Azerbaijan, Issue Mathematics, Series of Physical–Technical and Mathematical Sciences, v. 36 (1) 1, 100–111.
[17]	Najafov A. M., Kerbalayeva R. E. (2019) The embedding theorems for Besov-Morrey spaces of many groups of variables. Proceedings of A. Razmadze Institute Mathematics. Georgian Academy of Sciences, 26 (1), 125-131.
[18]	Perez C. (1991) Weighted norm inequality for general maximal operators. Publicacions Mathe., 35 (1), 169–186.
[19]	Taylor, M. (1994/1995) Microlocal analysis on Morrey spaces. Singularities and oscullations (Minneapolis). IMA 91, Math. Appl., Springer, New Yor., 97−135.

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Rena Eldar Kizi Kerbalayeva. (2021). Some Characterization of the Function Space Type of Lizorkin−Triebel−Morrey. Mathematics and Computer Science, 6(4), 59-64. https://doi.org/10.11648/j.mcs.20210604.11

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Rena Eldar Kizi Kerbalayeva. Some Characterization of the Function Space Type of Lizorkin−Triebel−Morrey. Math. Comput. Sci. 2021, 6(4), 59-64. doi: 10.11648/j.mcs.20210604.11

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AMA Style

Rena Eldar Kizi Kerbalayeva. Some Characterization of the Function Space Type of Lizorkin−Triebel−Morrey. Math Comput Sci. 2021;6(4):59-64. doi: 10.11648/j.mcs.20210604.11

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@article{10.11648/j.mcs.20210604.11,
  author = {Rena Eldar Kizi Kerbalayeva},
  title = {Some Characterization of the Function Space Type of Lizorkin−Triebel−Morrey},
  journal = {Mathematics and Computer Science},
  volume = {6},
  number = {4},
  pages = {59-64},
  doi = {10.11648/j.mcs.20210604.11},
  url = {https://doi.org/10.11648/j.mcs.20210604.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20210604.11},
  abstract = {This paper will introduce you to some properties of normed function spaces with many groups variables field of Analysis and it helps me appreciate how normed Lebesgue–Morrey space with many groups of variables that build and studied new normed spaces nowadays. Many of the topics here are important to an Analysis class. By reading this paper, you will discover the “embedding theory” of normed spaces type of Lebesgue–Morrey by introducing few of its “new functions with groups with variables” and along the way you will see to some interesting and article elements of the branch called Analysis. A lot of problems belonging to the characterization of various spaces of differentiability function spaces and relationships between them have been solved using the theory embedding theorems. The purpose of this paper is to review several embedding inequalities of normed spaces that will arise properties of these spaces and again throughout this material. We also give “working definition, notations” of a functions and function spaces. We must note that, the analysis is based on such function spaces to build new space type of Lizorkin–Triebel–Morrey. In addition, throughout this paper we will introduce a working normed function spaces type of Lizorkin–Triebel–Morrey with standard mathematical definitions and terminology. One aspect of this paper involves normed Lebesgue–Morey type spaces that can convert space from one to another.},
 year = {2021}
}

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TY  - JOUR
T1  - Some Characterization of the Function Space Type of Lizorkin−Triebel−Morrey
AU  - Rena Eldar Kizi Kerbalayeva
Y1  - 2021/08/30
PY  - 2021
N1  - https://doi.org/10.11648/j.mcs.20210604.11
DO  - 10.11648/j.mcs.20210604.11
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 59
EP  - 64
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20210604.11
AB  - This paper will introduce you to some properties of normed function spaces with many groups variables field of Analysis and it helps me appreciate how normed Lebesgue–Morrey space with many groups of variables that build and studied new normed spaces nowadays. Many of the topics here are important to an Analysis class. By reading this paper, you will discover the “embedding theory” of normed spaces type of Lebesgue–Morrey by introducing few of its “new functions with groups with variables” and along the way you will see to some interesting and article elements of the branch called Analysis. A lot of problems belonging to the characterization of various spaces of differentiability function spaces and relationships between them have been solved using the theory embedding theorems. The purpose of this paper is to review several embedding inequalities of normed spaces that will arise properties of these spaces and again throughout this material. We also give “working definition, notations” of a functions and function spaces. We must note that, the analysis is based on such function spaces to build new space type of Lizorkin–Triebel–Morrey. In addition, throughout this paper we will introduce a working normed function spaces type of Lizorkin–Triebel–Morrey with standard mathematical definitions and terminology. One aspect of this paper involves normed Lebesgue–Morey type spaces that can convert space from one to another.
VL  - 6
IS  - 4
ER  -

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Author Information

Rena Eldar Kizi Kerbalayeva

Institute of Mathematics and Mechanics, National Academy Science of Azerbaijan, Baku, Azerbaijan

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Plain Text BibTeX RIS

APA Style

Rena Eldar Kizi Kerbalayeva. (2021). Some Characterization of the Function Space Type of Lizorkin−Triebel−Morrey. Mathematics and Computer Science, 6(4), 59-64. https://doi.org/10.11648/j.mcs.20210604.11

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ACS Style

Rena Eldar Kizi Kerbalayeva. Some Characterization of the Function Space Type of Lizorkin−Triebel−Morrey. Math. Comput. Sci. 2021, 6(4), 59-64. doi: 10.11648/j.mcs.20210604.11

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AMA Style

Rena Eldar Kizi Kerbalayeva. Some Characterization of the Function Space Type of Lizorkin−Triebel−Morrey. Math Comput Sci. 2021;6(4):59-64. doi: 10.11648/j.mcs.20210604.11

Copy | Download

@article{10.11648/j.mcs.20210604.11,
  author = {Rena Eldar Kizi Kerbalayeva},
  title = {Some Characterization of the Function Space Type of Lizorkin−Triebel−Morrey},
  journal = {Mathematics and Computer Science},
  volume = {6},
  number = {4},
  pages = {59-64},
  doi = {10.11648/j.mcs.20210604.11},
  url = {https://doi.org/10.11648/j.mcs.20210604.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20210604.11},
  abstract = {This paper will introduce you to some properties of normed function spaces with many groups variables field of Analysis and it helps me appreciate how normed Lebesgue–Morrey space with many groups of variables that build and studied new normed spaces nowadays. Many of the topics here are important to an Analysis class. By reading this paper, you will discover the “embedding theory” of normed spaces type of Lebesgue–Morrey by introducing few of its “new functions with groups with variables” and along the way you will see to some interesting and article elements of the branch called Analysis. A lot of problems belonging to the characterization of various spaces of differentiability function spaces and relationships between them have been solved using the theory embedding theorems. The purpose of this paper is to review several embedding inequalities of normed spaces that will arise properties of these spaces and again throughout this material. We also give “working definition, notations” of a functions and function spaces. We must note that, the analysis is based on such function spaces to build new space type of Lizorkin–Triebel–Morrey. In addition, throughout this paper we will introduce a working normed function spaces type of Lizorkin–Triebel–Morrey with standard mathematical definitions and terminology. One aspect of this paper involves normed Lebesgue–Morey type spaces that can convert space from one to another.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Some Characterization of the Function Space Type of Lizorkin−Triebel−Morrey
AU  - Rena Eldar Kizi Kerbalayeva
Y1  - 2021/08/30
PY  - 2021
N1  - https://doi.org/10.11648/j.mcs.20210604.11
DO  - 10.11648/j.mcs.20210604.11
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 59
EP  - 64
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20210604.11
AB  - This paper will introduce you to some properties of normed function spaces with many groups variables field of Analysis and it helps me appreciate how normed Lebesgue–Morrey space with many groups of variables that build and studied new normed spaces nowadays. Many of the topics here are important to an Analysis class. By reading this paper, you will discover the “embedding theory” of normed spaces type of Lebesgue–Morrey by introducing few of its “new functions with groups with variables” and along the way you will see to some interesting and article elements of the branch called Analysis. A lot of problems belonging to the characterization of various spaces of differentiability function spaces and relationships between them have been solved using the theory embedding theorems. The purpose of this paper is to review several embedding inequalities of normed spaces that will arise properties of these spaces and again throughout this material. We also give “working definition, notations” of a functions and function spaces. We must note that, the analysis is based on such function spaces to build new space type of Lizorkin–Triebel–Morrey. In addition, throughout this paper we will introduce a working normed function spaces type of Lizorkin–Triebel–Morrey with standard mathematical definitions and terminology. One aspect of this paper involves normed Lebesgue–Morey type spaces that can convert space from one to another.
VL  - 6
IS  - 4
ER  -

Copy | Download