Research Article
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Year 2022, Issue: 40, 74 - 81, 30.09.2022

Merve Esra Türkay

https://doi.org/10.53570/jnt.1162966
Cited By: 1

Abstract

References

  • V. S. Guliyev, J. J. Hasanov, Y. Zeren, Necessary and Sufficient Conditions for the Boundedness of Riesz Potential in the Modified Morrey Spaces, Journal of Mathematical Inequalities 5 (4) (2011) 491-506.
  • V. S. Guliyev, K. Rahimova, Parabolic Fractional Integral Operator in Modified Parabolic Morrey Spaces, Proceedings Razmadze Mathematical Institute 163 (2013) 85-106.
  • V. Guliyev, H. Armutcu, T. Azeroglu, Characterizations for the Potential Operators on Carleson Curves in Local Generalized Morrey Spaces, Open Mathematics 18 (1) (2020), 1317-1331.
  • C. B. Morrey, On the Solutions of Quasi-Linear Elliptic Partial Differential Equations, Transactions of the American Mathematical Society 43 (1938) 126-166.
  • N. Samko, Weighted Hardy and Singular Operators in Morrey Spaces, Journal of Mathematical Analysis and Applications 350 (1) (2009) 56-72.
  • A. Böttcher, Y. I. Karlovich, Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators, 15, Springer Science Business Media, 1997.
  • I. B. Dadashova, C. Aykol, Z. Cakir, A. Serbetci, Potential Operators in Modified Morrey Spaces Defined on Carleson Curves, Transactions of A. Razmadze Mathematical Institute 172 (1) (2018) 15-29.
  • J. I Mamedkhanov, I. B. Dadashova, Some Properties of the Potential Operators in Morrey Spaces Defined on Carleson Curves, Complex Variables and Elliptic Equations 55 (8-10) (2010) 937-945.
  • M. E. Türkay, M. Mursaleen, Some Estimates in Lp(Γ) for Maximal Commutator and Commutator of Maximal Function (2022) In Press.
  • L. Grafakos, Modern Fourier Analysis, 2nd ed., Graduate Texts in Mathematics, 250, Springer, New York 2009.
  • A. Kufner, O. John, S. Fucik, Function Spaces, Noordhoff, Leyden, and Academia, Prague 1977.
  • E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, 43, Princeton University Press, Princeton, NJ 1993.
  • M. Agcayazi, A. Gogatishvili, K. Koca, R. Mustafayev, A Note on Maximal Commutators and Commutators of Maximal Functions, Journal of the Mathematical Society of Japan 67 (2) (2015) 581-593.
  • C. Aykol, H. Armutcu, M. N. Omarova, Maximal Commutator and Commutator of Maximal Function on Modified Morrey Spaces, Transactions of NAS of Azerbaijan, Issue Mathematics 36 (2016) 29-35.
  • J. Bastero, Milman M. and Ruiz F.J., Commutators for the Maximal and Sharp Functions, Proceedings of the American Mathematical Society 128 (11) (2000) 3329-3334.
  • A. Bonami, T. Iwaniec, P. Jones, M. Zinsmeister, On the Product of Functions in BMO and $H_1$, Annales De L'institut Fourier (Grenoble) 57 (5) (2007) 1405-1439.
  • J. Garcia-Cuerva, E. Harboure, C. Segovia, J. L. Torrea, Weighted Norm Inequalities for Commutators of Strongly Singular Integrals, Indiana University Mathematics Journal 40 (4) (1991) 1397-1420.
  • A. Gogatishvili, R.Ch. Mustafayev, M. Agcayazi, Weak-Type Estimates in Morrey Spaces for Maximal Commutator and Commutator of Maximal Function Tokyo Journal of Mathematics 41 (1) (2018) 193-218.
  • D. Li, G. Hu, X. Shi, Weighted Norm Inequalities for the Maximal Commutators of Singular Integral Operators, Journal of Mathematical Analysis and Applications 319 (2) (2006) 509-521.
  • M. Milman, T. Schonbek, Second Order Estimates in Interpolation Theory and Applications, Proceedings of the American Mathematical Society 110 (4) (1990) 961-969.
  • C. Segovia, J. L. Torrea, Higher Order Commutators for Vector-Valued Calderon-Zygmund Operators, Transactions of the American Mathematical Society 336 (2) (1993) 537-556.
  • C. P. Xie, Some Estimates of Commutators, Real Analysis Exchange 36 (2) (2010) 405-415.

Some New Estimates for Maximal Commutator and Commutator of Maximal Function in $L_{p,\lambda}(\Gamma)$

Year 2022, Issue: 40, 74 - 81, 30.09.2022

Merve Esra Türkay

https://doi.org/10.53570/jnt.1162966
Cited By: 1

Abstract

The theory of boundedness of classical operators of real analyses on Morrey spaces defined on Carleson curves has made significant progress in recent years as it allows for various applications. This study obtains new estimates about the boundedness of the maximal commutator operator $M_b$ and the commutator of the maximal function $[M, b]$ in Morrey spaces defined on Carleson curves.

Keywords

Maximal commutator . Commutator of maximal function . Morrey space . BMO

References

  • V. S. Guliyev, J. J. Hasanov, Y. Zeren, Necessary and Sufficient Conditions for the Boundedness of Riesz Potential in the Modified Morrey Spaces, Journal of Mathematical Inequalities 5 (4) (2011) 491-506.
  • V. S. Guliyev, K. Rahimova, Parabolic Fractional Integral Operator in Modified Parabolic Morrey Spaces, Proceedings Razmadze Mathematical Institute 163 (2013) 85-106.
  • V. Guliyev, H. Armutcu, T. Azeroglu, Characterizations for the Potential Operators on Carleson Curves in Local Generalized Morrey Spaces, Open Mathematics 18 (1) (2020), 1317-1331.
  • C. B. Morrey, On the Solutions of Quasi-Linear Elliptic Partial Differential Equations, Transactions of the American Mathematical Society 43 (1938) 126-166.
  • N. Samko, Weighted Hardy and Singular Operators in Morrey Spaces, Journal of Mathematical Analysis and Applications 350 (1) (2009) 56-72.
  • A. Böttcher, Y. I. Karlovich, Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators, 15, Springer Science Business Media, 1997.
  • I. B. Dadashova, C. Aykol, Z. Cakir, A. Serbetci, Potential Operators in Modified Morrey Spaces Defined on Carleson Curves, Transactions of A. Razmadze Mathematical Institute 172 (1) (2018) 15-29.
  • J. I Mamedkhanov, I. B. Dadashova, Some Properties of the Potential Operators in Morrey Spaces Defined on Carleson Curves, Complex Variables and Elliptic Equations 55 (8-10) (2010) 937-945.
  • M. E. Türkay, M. Mursaleen, Some Estimates in Lp(Γ) for Maximal Commutator and Commutator of Maximal Function (2022) In Press.
  • L. Grafakos, Modern Fourier Analysis, 2nd ed., Graduate Texts in Mathematics, 250, Springer, New York 2009.
  • A. Kufner, O. John, S. Fucik, Function Spaces, Noordhoff, Leyden, and Academia, Prague 1977.
  • E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, 43, Princeton University Press, Princeton, NJ 1993.
  • M. Agcayazi, A. Gogatishvili, K. Koca, R. Mustafayev, A Note on Maximal Commutators and Commutators of Maximal Functions, Journal of the Mathematical Society of Japan 67 (2) (2015) 581-593.
  • C. Aykol, H. Armutcu, M. N. Omarova, Maximal Commutator and Commutator of Maximal Function on Modified Morrey Spaces, Transactions of NAS of Azerbaijan, Issue Mathematics 36 (2016) 29-35.
  • J. Bastero, Milman M. and Ruiz F.J., Commutators for the Maximal and Sharp Functions, Proceedings of the American Mathematical Society 128 (11) (2000) 3329-3334.
  • A. Bonami, T. Iwaniec, P. Jones, M. Zinsmeister, On the Product of Functions in BMO and $H_1$, Annales De L'institut Fourier (Grenoble) 57 (5) (2007) 1405-1439.
  • J. Garcia-Cuerva, E. Harboure, C. Segovia, J. L. Torrea, Weighted Norm Inequalities for Commutators of Strongly Singular Integrals, Indiana University Mathematics Journal 40 (4) (1991) 1397-1420.
  • A. Gogatishvili, R.Ch. Mustafayev, M. Agcayazi, Weak-Type Estimates in Morrey Spaces for Maximal Commutator and Commutator of Maximal Function Tokyo Journal of Mathematics 41 (1) (2018) 193-218.
  • D. Li, G. Hu, X. Shi, Weighted Norm Inequalities for the Maximal Commutators of Singular Integral Operators, Journal of Mathematical Analysis and Applications 319 (2) (2006) 509-521.
  • M. Milman, T. Schonbek, Second Order Estimates in Interpolation Theory and Applications, Proceedings of the American Mathematical Society 110 (4) (1990) 961-969.
  • C. Segovia, J. L. Torrea, Higher Order Commutators for Vector-Valued Calderon-Zygmund Operators, Transactions of the American Mathematical Society 336 (2) (1993) 537-556.
  • C. P. Xie, Some Estimates of Commutators, Real Analysis Exchange 36 (2) (2010) 405-415.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Merve Esra Türkay 0000-0003-4429-2685

Publication Date September 30, 2022
Submission Date August 16, 2022
Published in Issue Year 2022 Issue: 40

Cite

APA Türkay, M. E. (2022). Some New Estimates for Maximal Commutator and Commutator of Maximal Function in $L_{p,\lambda}(\Gamma)$. Journal of New Theory(40), 74-81. https://doi.org/10.53570/jnt.1162966
AMA Türkay ME. Some New Estimates for Maximal Commutator and Commutator of Maximal Function in $L_{p,\lambda}(\Gamma)$. JNT. September 2022;(40):74-81. doi:10.53570/jnt.1162966
Chicago Türkay, Merve Esra. “Some New Estimates for Maximal Commutator and Commutator of Maximal Function in $L_{p,\lambda}(\Gamma)$”. Journal of New Theory, no. 40 (September 2022): 74-81. https://doi.org/10.53570/jnt.1162966.
EndNote Türkay ME (September 1, 2022) Some New Estimates for Maximal Commutator and Commutator of Maximal Function in $L_{p,\lambda}(\Gamma)$. Journal of New Theory 40 74–81.
IEEE M. E. Türkay, “Some New Estimates for Maximal Commutator and Commutator of Maximal Function in $L_{p,\lambda}(\Gamma)$”, JNT, no. 40, pp. 74–81, September 2022, doi: 10.53570/jnt.1162966.
ISNAD Türkay, Merve Esra. “Some New Estimates for Maximal Commutator and Commutator of Maximal Function in $L_{p,\lambda}(\Gamma)$”. Journal of New Theory 40 (September 2022), 74-81. https://doi.org/10.53570/jnt.1162966.
JAMA Türkay ME. Some New Estimates for Maximal Commutator and Commutator of Maximal Function in $L_{p,\lambda}(\Gamma)$. JNT. 2022;:74–81.
MLA Türkay, Merve Esra. “Some New Estimates for Maximal Commutator and Commutator of Maximal Function in $L_{p,\lambda}(\Gamma)$”. Journal of New Theory, no. 40, 2022, pp. 74-81, doi:10.53570/jnt.1162966.
Vancouver Türkay ME. Some New Estimates for Maximal Commutator and Commutator of Maximal Function in $L_{p,\lambda}(\Gamma)$. JNT. 2022(40):74-81.

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Some New Estimates for Maximal Commutator and Commutator of Maximal Function in $L_{p,\lambda}(\Gamma)$
Journal of New Theory
https://doi.org/10.53570/jnt.1162966
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