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A_{p1,q1}^{p2,q2}(G,w) Banach Uzayı Üzerindeki Bazı Yeni Sonuçlar

Year 2021, Volume: 9 Issue: 4, 1420 - 1435, 31.07.2021
https://doi.org/10.29130/dubited.866704

Abstract

G ünimodüler yerel kompakt grup ve p=min{p1,p2} olmak üzere w∈Bp olsun. Bu çalışmada, A_{p1,q1}^{p2,q2}(G,w) uzayının indislerin değişmesi durumunda kapsama özellikleri incelenmiştir. Ayrıca w ağırlığının bazı özel şartları sağlaması durumunda A_{p1,q1}^{p2,q2}(G,w) uzayı için Λ_G^1 (w) ağırlıklı Lorentz uzayında bir yaklaşık birim elde edilmiş ve A_{p1,q1}^{p2,q2}(G,w) uzayının bir Banach sağ Λ_G^1 (w)-modül olduğu ispatlanmıştır.

References

  • [1] G. G. Lorentz, “Some new functional spaces,” Annals of Mathematics, c. 51, s. 1, ss. 37-55, 1950.
  • [2] G. G. Lorentz, “On the theory of spaces Λ ,” Pacific Journal of Mathematics, c. 1, s. 3, ss. 411-429, 1951.
  • [3] P. L. Butzer, H. Berens, Semi-groups of Operators and Approximation, Berlin-Heidelberg-New York, Springer-Verlag, 1967.
  • [4] J. Bergh, J. Liifstrtim, Interpolation Spaces, An Introduction, Berlin-Heidelberg-New York, Springer-Verlag, 1976.
  • [5] J. Creekmore, Geometry of Lorentz spaces, Ph.D. Dissertation, Kent State University, 1979.
  • [6] S. Reisner, “A factorization theorem in Banach lattices and its application to Lorentz spaces,” Annales de l'institut Fourier. c. 31, s. 1, ss. 239-255, 1981.
  • [7] H. Avcı, A. T. Gürkanlı, “Multipliers and tensor products of L(p,q) Lorentz spaces,” Acta Mathematica Scientia, c. 27(B), s. 1, ss. 107-116, 2007.
  • [8] H. Li, Q. Sun, “Multipliers and Tensor Products of the Weighted Lorentz Spaces Λ_G^{p,q}(w),'' Georgian Mathematical Journal, c. 19, ss. 721-740, 2012.
  • [9] M. J. Carro, J. A. Raposo, J. Soria, Recent Developments in the Theory of Lorentz Spaces and Weighted Inequalities, American Mathematical Society, 2007.
  • [10] N. Değirmen, İ. Değirmen, “A_{p1,q1}^{p2,q2}(G,w) Uzayı ve Bazı Topolojik Özellikleri Üzerine,” Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 11, s. 2, ss. 1468-1480, 2021.
  • [11] F. F. Bonsall, J. Duncan, Complete Normed Algebras, Springer Verlag, Berlin, 1973.
  • [12] R. S. Doran, J. Wichmann, Approximate Identities and Factorization in Banach Modules, Lecture Notes in Mathematics,768, Springer Verlag, 1979.
  • [13] L. Y. H. Yap, “Some Remarks on Convolution Operators and L(p,q) Spaces,” Duke Mathematical Journal, c. 36, ss. 647-658, 1969.
  • [14] R. Hunt, “On L(p,q) Spaces,” L'Enseignement Mathématique, c. 12, ss. 249-276, 1966.
  • [15] M. J. Carro, A. Garcia del Amo, J. Soria, “Weak-Type Weights and Normable Lorentz Spaces,” Proceedings of the American Mathematical Society, c. 124, s. 3, ss. 849-857, 1996.
  • [16] C. J. Neugebauer, “Weighted Norm Inequalities for Averaging Operators of Monotone Functions,” Publicacions Matematiques, c. 35, ss. 429-447, 1991.
  • [17] M. A. Arino, B. Muckenhoupt, “Maximal Functions Classical Lorentz Spaces and Hardy's Inequality with Weights for Nonincreasing Functions,” Transactions of the American Mathematical Society, c. 320, s. 2, ss. 727-735, 1990.
  • [18] G. B. Folland, A Course in Abstract Harmonic Analysis, CRS Press, Boca Raton, Florida, 1995.
  • [19] P. R. Halmos, Measure Theory, 2. baskı, Springer Verlag, New York, 1974.

Some New Results on the Banach Space A_{p1,q1}^{p2,q2}(G,w)

Year 2021, Volume: 9 Issue: 4, 1420 - 1435, 31.07.2021
https://doi.org/10.29130/dubited.866704

Abstract

Let G be a unimodular locally compact group and w∈Bp where p=min{p1,p2} . In this work, in the case of changing indices, the inclusion properties of the space A_{p1,q1}^{p2,q2}(G,w) have been examined. Also, if the weight w provides some special conditions, an approximate identity for the space A_{p1,q1}^{p2,q2}(G,w) has been obtained in the weighted Lorentz space Λ_G^1 (w) and it has been proved that the space A_{p1,q1}^{p2,q2}(G,w) is a Banach right Λ_G^1 (w)-module.

References

  • [1] G. G. Lorentz, “Some new functional spaces,” Annals of Mathematics, c. 51, s. 1, ss. 37-55, 1950.
  • [2] G. G. Lorentz, “On the theory of spaces Λ ,” Pacific Journal of Mathematics, c. 1, s. 3, ss. 411-429, 1951.
  • [3] P. L. Butzer, H. Berens, Semi-groups of Operators and Approximation, Berlin-Heidelberg-New York, Springer-Verlag, 1967.
  • [4] J. Bergh, J. Liifstrtim, Interpolation Spaces, An Introduction, Berlin-Heidelberg-New York, Springer-Verlag, 1976.
  • [5] J. Creekmore, Geometry of Lorentz spaces, Ph.D. Dissertation, Kent State University, 1979.
  • [6] S. Reisner, “A factorization theorem in Banach lattices and its application to Lorentz spaces,” Annales de l'institut Fourier. c. 31, s. 1, ss. 239-255, 1981.
  • [7] H. Avcı, A. T. Gürkanlı, “Multipliers and tensor products of L(p,q) Lorentz spaces,” Acta Mathematica Scientia, c. 27(B), s. 1, ss. 107-116, 2007.
  • [8] H. Li, Q. Sun, “Multipliers and Tensor Products of the Weighted Lorentz Spaces Λ_G^{p,q}(w),'' Georgian Mathematical Journal, c. 19, ss. 721-740, 2012.
  • [9] M. J. Carro, J. A. Raposo, J. Soria, Recent Developments in the Theory of Lorentz Spaces and Weighted Inequalities, American Mathematical Society, 2007.
  • [10] N. Değirmen, İ. Değirmen, “A_{p1,q1}^{p2,q2}(G,w) Uzayı ve Bazı Topolojik Özellikleri Üzerine,” Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 11, s. 2, ss. 1468-1480, 2021.
  • [11] F. F. Bonsall, J. Duncan, Complete Normed Algebras, Springer Verlag, Berlin, 1973.
  • [12] R. S. Doran, J. Wichmann, Approximate Identities and Factorization in Banach Modules, Lecture Notes in Mathematics,768, Springer Verlag, 1979.
  • [13] L. Y. H. Yap, “Some Remarks on Convolution Operators and L(p,q) Spaces,” Duke Mathematical Journal, c. 36, ss. 647-658, 1969.
  • [14] R. Hunt, “On L(p,q) Spaces,” L'Enseignement Mathématique, c. 12, ss. 249-276, 1966.
  • [15] M. J. Carro, A. Garcia del Amo, J. Soria, “Weak-Type Weights and Normable Lorentz Spaces,” Proceedings of the American Mathematical Society, c. 124, s. 3, ss. 849-857, 1996.
  • [16] C. J. Neugebauer, “Weighted Norm Inequalities for Averaging Operators of Monotone Functions,” Publicacions Matematiques, c. 35, ss. 429-447, 1991.
  • [17] M. A. Arino, B. Muckenhoupt, “Maximal Functions Classical Lorentz Spaces and Hardy's Inequality with Weights for Nonincreasing Functions,” Transactions of the American Mathematical Society, c. 320, s. 2, ss. 727-735, 1990.
  • [18] G. B. Folland, A Course in Abstract Harmonic Analysis, CRS Press, Boca Raton, Florida, 1995.
  • [19] P. R. Halmos, Measure Theory, 2. baskı, Springer Verlag, New York, 1974.
There are 19 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Nilay Değirmen 0000-0001-8192-8473

Publication Date July 31, 2021
Published in Issue Year 2021 Volume: 9 Issue: 4

Cite

APA Değirmen, N. (2021). A_{p1,q1}^{p2,q2}(G,w) Banach Uzayı Üzerindeki Bazı Yeni Sonuçlar. Duzce University Journal of Science and Technology, 9(4), 1420-1435. https://doi.org/10.29130/dubited.866704
AMA Değirmen N. A_{p1,q1}^{p2,q2}(G,w) Banach Uzayı Üzerindeki Bazı Yeni Sonuçlar. DUBİTED. July 2021;9(4):1420-1435. doi:10.29130/dubited.866704
Chicago Değirmen, Nilay. “A_{p1,q1}^{p2,q2}(G,w) Banach Uzayı Üzerindeki Bazı Yeni Sonuçlar”. Duzce University Journal of Science and Technology 9, no. 4 (July 2021): 1420-35. https://doi.org/10.29130/dubited.866704.
EndNote Değirmen N (July 1, 2021) A_{p1,q1}^{p2,q2}(G,w) Banach Uzayı Üzerindeki Bazı Yeni Sonuçlar. Duzce University Journal of Science and Technology 9 4 1420–1435.
IEEE N. Değirmen, “A_{p1,q1}^{p2,q2}(G,w) Banach Uzayı Üzerindeki Bazı Yeni Sonuçlar”, DUBİTED, vol. 9, no. 4, pp. 1420–1435, 2021, doi: 10.29130/dubited.866704.
ISNAD Değirmen, Nilay. “A_{p1,q1}^{p2,q2}(G,w) Banach Uzayı Üzerindeki Bazı Yeni Sonuçlar”. Duzce University Journal of Science and Technology 9/4 (July 2021), 1420-1435. https://doi.org/10.29130/dubited.866704.
JAMA Değirmen N. A_{p1,q1}^{p2,q2}(G,w) Banach Uzayı Üzerindeki Bazı Yeni Sonuçlar. DUBİTED. 2021;9:1420–1435.
MLA Değirmen, Nilay. “A_{p1,q1}^{p2,q2}(G,w) Banach Uzayı Üzerindeki Bazı Yeni Sonuçlar”. Duzce University Journal of Science and Technology, vol. 9, no. 4, 2021, pp. 1420-35, doi:10.29130/dubited.866704.
Vancouver Değirmen N. A_{p1,q1}^{p2,q2}(G,w) Banach Uzayı Üzerindeki Bazı Yeni Sonuçlar. DUBİTED. 2021;9(4):1420-35.