Research Article
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Year 2019, Volume: 2 Issue: 3, 148 - 151, 30.09.2019
https://doi.org/10.32323/ujma.522420

Abstract

References

  • [1] S. Lu, D. Yang and G. Hu, Herz Type Spaces and Their Applications, Science Press, Beijing, 2008.
  • [2] J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North–Holland Mathematics Studies 116, North–Holland Publishing Co., Amsterdam, 1985.
  • [3] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226.
  • [4] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Pure and Applied Mathematics 123, Academic Press, Inc., Orlando, FL, 1986.
  • [5] M. Izuki and Y. Sawano, The Haar wavelet characterization of weighted Herz spaces and greediness of the Haar wavelet basis, J. Math. Anal. Appl. 362(1) (2010), 140–155.
  • [6] M. Izuki and K. Tachizawa, Wavelet characterizations of weighted Herz spaces, Sci. Math. Jpn. 67(3)(2008), 353–363.
  • [7] S. Lu, K. Yabuta and D. Yang, Boundedness of some sublinear operators in weighted Herz-type spaces, Kodai Math. J. 23(3)(2000), 391–410.
  • [8] K. Matsuoka, On some weighted Herz spaces and the Hardy–Littlewood maximal operator, in: Proceedings of the International Symposium on Banach and Function Spaces II (Kitakyusyu, Japan, 2006), M. Kato et al. (eds.), pp. 375–384, Yokohama Publ., Yokohama, 2008.
  • [9] A. Almeida and D. Drihem, Maximal, potential and singular type operators on Herz spaces with variable exponents, J. Math.Anal. Appl. 394(2)(2012), 781–795.
  • [10] M. Izuki and T. Noi, Duality of Besov, Triebel-Lizorkin and Herz spaces with variable exponents, Rend. Circ. Mat. Palermo (2) 63(2)(2014),221-245.
  • [11] M. Izuki and T. Noi, Hardy spaces associated to critical Herz spaces with variable exponent, Mediterranean J. Math.13(5)(2016), 29813013.
  • [12] D. Cruz-Uribe, L. Diening and P. Hasto, The maximal operator on weighted variable Lebesgue spaces, Fract. Calc. Appl. Anal. 14(3)(2011), 361-374.
  • [13] D. Cruz-Uribe, A. Fiorenza and C. J. Neugebauer, Weighted norm inequalities for the maximal operator on variable Lebesgue spaces, J. Math. Anal. Appl. 394(2)(2012), 744-760.
  • [14] D. Cruz-Uribe, SFO and D.Wang, Extrapolation and weighted norm inequalities in the variable Lebesgue spaces, Trans. Amer. Math Soc. 369(2)(2017), 1205-1235.
  • [15] L. Diening and P. Hasto, Muckenhoupt weights in variable exponent spaces, preprint, available at htt p : www:helsinki:=hasto=pp=p75submit:pd f
  • [16] F. I. Mamedov, Y. Zeren and L. Akin, Compactification of weighred Hardy operator in variable exponent Lebesgue spaces, Asian J. Math. Comp. Res., 17(1)(2017), 38-47.
  • [17] J. Garca-Cuerva, Hardy spaces and Beurling algebras, J. London Math. Soc. (2) 39(3)(1989), 499-513.
  • [18] L. Akin, A Characterization of Approximation of Hardy Operators in VLS, Celal Bayar University Journal of Science, 14(3)(2018), 333-336.
  • [19] L. Akin, On two weight criterions for the Hardy-Littlewood maximal operator in BFS, Asian J. Sci. Tech., 09 (5)(2018), 8085-8089.

On Some Properties of Integral-Type Operator in Weighted Herz Spaces with Variable Exponent Lebesgue Spaces

Year 2019, Volume: 2 Issue: 3, 148 - 151, 30.09.2019
https://doi.org/10.32323/ujma.522420

Abstract

For the last quarter century a considerable number of research has been carried out on the study of Herz spaces, variable exponent Lebesgue  spaces and Sobolev spaces. This studies also have played an important role in  problems of elasticity, fluid dynamics, calculus of variations. Our aim in this work is to prove some properties of the integral-type operator on weighted Herz space with variable exponent Lebesgue space (VELS).

References

  • [1] S. Lu, D. Yang and G. Hu, Herz Type Spaces and Their Applications, Science Press, Beijing, 2008.
  • [2] J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North–Holland Mathematics Studies 116, North–Holland Publishing Co., Amsterdam, 1985.
  • [3] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226.
  • [4] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Pure and Applied Mathematics 123, Academic Press, Inc., Orlando, FL, 1986.
  • [5] M. Izuki and Y. Sawano, The Haar wavelet characterization of weighted Herz spaces and greediness of the Haar wavelet basis, J. Math. Anal. Appl. 362(1) (2010), 140–155.
  • [6] M. Izuki and K. Tachizawa, Wavelet characterizations of weighted Herz spaces, Sci. Math. Jpn. 67(3)(2008), 353–363.
  • [7] S. Lu, K. Yabuta and D. Yang, Boundedness of some sublinear operators in weighted Herz-type spaces, Kodai Math. J. 23(3)(2000), 391–410.
  • [8] K. Matsuoka, On some weighted Herz spaces and the Hardy–Littlewood maximal operator, in: Proceedings of the International Symposium on Banach and Function Spaces II (Kitakyusyu, Japan, 2006), M. Kato et al. (eds.), pp. 375–384, Yokohama Publ., Yokohama, 2008.
  • [9] A. Almeida and D. Drihem, Maximal, potential and singular type operators on Herz spaces with variable exponents, J. Math.Anal. Appl. 394(2)(2012), 781–795.
  • [10] M. Izuki and T. Noi, Duality of Besov, Triebel-Lizorkin and Herz spaces with variable exponents, Rend. Circ. Mat. Palermo (2) 63(2)(2014),221-245.
  • [11] M. Izuki and T. Noi, Hardy spaces associated to critical Herz spaces with variable exponent, Mediterranean J. Math.13(5)(2016), 29813013.
  • [12] D. Cruz-Uribe, L. Diening and P. Hasto, The maximal operator on weighted variable Lebesgue spaces, Fract. Calc. Appl. Anal. 14(3)(2011), 361-374.
  • [13] D. Cruz-Uribe, A. Fiorenza and C. J. Neugebauer, Weighted norm inequalities for the maximal operator on variable Lebesgue spaces, J. Math. Anal. Appl. 394(2)(2012), 744-760.
  • [14] D. Cruz-Uribe, SFO and D.Wang, Extrapolation and weighted norm inequalities in the variable Lebesgue spaces, Trans. Amer. Math Soc. 369(2)(2017), 1205-1235.
  • [15] L. Diening and P. Hasto, Muckenhoupt weights in variable exponent spaces, preprint, available at htt p : www:helsinki:=hasto=pp=p75submit:pd f
  • [16] F. I. Mamedov, Y. Zeren and L. Akin, Compactification of weighred Hardy operator in variable exponent Lebesgue spaces, Asian J. Math. Comp. Res., 17(1)(2017), 38-47.
  • [17] J. Garca-Cuerva, Hardy spaces and Beurling algebras, J. London Math. Soc. (2) 39(3)(1989), 499-513.
  • [18] L. Akin, A Characterization of Approximation of Hardy Operators in VLS, Celal Bayar University Journal of Science, 14(3)(2018), 333-336.
  • [19] L. Akin, On two weight criterions for the Hardy-Littlewood maximal operator in BFS, Asian J. Sci. Tech., 09 (5)(2018), 8085-8089.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Lütfi Akın 0000-0002-5653-9393

Publication Date September 30, 2019
Submission Date February 5, 2019
Acceptance Date July 3, 2019
Published in Issue Year 2019 Volume: 2 Issue: 3

Cite

APA Akın, L. (2019). On Some Properties of Integral-Type Operator in Weighted Herz Spaces with Variable Exponent Lebesgue Spaces. Universal Journal of Mathematics and Applications, 2(3), 148-151. https://doi.org/10.32323/ujma.522420
AMA Akın L. On Some Properties of Integral-Type Operator in Weighted Herz Spaces with Variable Exponent Lebesgue Spaces. Univ. J. Math. Appl. September 2019;2(3):148-151. doi:10.32323/ujma.522420
Chicago Akın, Lütfi. “On Some Properties of Integral-Type Operator in Weighted Herz Spaces With Variable Exponent Lebesgue Spaces”. Universal Journal of Mathematics and Applications 2, no. 3 (September 2019): 148-51. https://doi.org/10.32323/ujma.522420.
EndNote Akın L (September 1, 2019) On Some Properties of Integral-Type Operator in Weighted Herz Spaces with Variable Exponent Lebesgue Spaces. Universal Journal of Mathematics and Applications 2 3 148–151.
IEEE L. Akın, “On Some Properties of Integral-Type Operator in Weighted Herz Spaces with Variable Exponent Lebesgue Spaces”, Univ. J. Math. Appl., vol. 2, no. 3, pp. 148–151, 2019, doi: 10.32323/ujma.522420.
ISNAD Akın, Lütfi. “On Some Properties of Integral-Type Operator in Weighted Herz Spaces With Variable Exponent Lebesgue Spaces”. Universal Journal of Mathematics and Applications 2/3 (September 2019), 148-151. https://doi.org/10.32323/ujma.522420.
JAMA Akın L. On Some Properties of Integral-Type Operator in Weighted Herz Spaces with Variable Exponent Lebesgue Spaces. Univ. J. Math. Appl. 2019;2:148–151.
MLA Akın, Lütfi. “On Some Properties of Integral-Type Operator in Weighted Herz Spaces With Variable Exponent Lebesgue Spaces”. Universal Journal of Mathematics and Applications, vol. 2, no. 3, 2019, pp. 148-51, doi:10.32323/ujma.522420.
Vancouver Akın L. On Some Properties of Integral-Type Operator in Weighted Herz Spaces with Variable Exponent Lebesgue Spaces. Univ. J. Math. Appl. 2019;2(3):148-51.

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