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

Lütfi Akın

doi:10.32323/ujma.522420

EN

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

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).

Keywords

Variable exponent,Herz space,Operator theory

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.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Lütfi Akın
0000-0002-5653-9393
Türkiye

Publication Date

September 30, 2019

Submission Date

February 5, 2019

Acceptance Date

July 3, 2019

Published in Issue

Year 2019 Volume: 2 Number: 3

DOI

https://doi.org/10.32323/ujma.522420

IZ

https://izlik.org/JA78TC39BB

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

1.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):148-151. doi:10.32323/ujma.522420

Chicago

Akın, Lütfi. 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): 148-51. 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

[1]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, Sept. 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 1, 2019): 148-151. https://doi.org/10.32323/ujma.522420.

JAMA

1.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, Sept. 2019, pp. 148-51, doi:10.32323/ujma.522420.

Vancouver

1.Lütfi Akın. On Some Properties of Integral-Type Operator in Weighted Herz Spaces with Variable Exponent Lebesgue Spaces. Univ. J. Math. Appl. 2019 Sep. 1;2(3):148-51. doi:10.32323/ujma.522420