Research ArticleOpen AccessGoogle Scholar indexed
Boundedness of Rough Operators on Grand Variable Herz Spaces
Faculty of Sciences and Technology, Adam Barka University of Abeche, Abeche, Chad
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
Faculty of Education, Sudan University of Science and Technology, Khartoum, Khartoum State, Sudan
- 1 Faculty of Sciences and Technology, Adam Barka University of Abeche, Abeche, Chad
- 2 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 3 Faculty of Education, Sudan University of Science and Technology, Khartoum, Khartoum State, Sudan
Copy link · social · email
Abstract
In this paper, we prove the boundedness of Calderón-Zygmund singular integral operators T Ω on grand Herz spaces with variable exponent under some conditions.
KeywordsCalderón-Zygmund Singular Integral OperatorGrand Herz SpacesVariable Exponent
- Kováčik, O. and Rákosník, J. (1991) On Spaces L p ( x ) and W k , p ( x ) , Czechoslovak Mathematical Journal, 41, 592-618. https://doi.org/10.21136/CMJ.1991.102493
- Calderón, A.P. and Zygmund, A. (1952) On the Existence of Certain Singular Integrals. Acta Mathematica, 88, 85-139. https://doi.org/10.1007/BF02392130
- Calderón, A.P. and Zygmund, A. (1956) On Singular Integrals. American Journal of Mathematics, 78, 289-309. https://doi.org/10.2307/2372517
- Lu, S.Y. and Yang, D.C. (1997) The Continuity of Commutators on Herz-Type Spaces. The Michigan Mathematical Journal, 44, 255-281. https://doi.org/10.1307/mmj/1029005703
- Shanzhen, L., Yong, D. and Dunyan, Y. (2007) Singular Integrals and Related Topics. World Scientific, Singapore.
- Rafeiro, H., Samko, S. and Umarkhadzhiev, S. (2018) Grand Lebesgue Sequence Spaces. Georgian Mathematical Journal, 25, 291-302. https://doi.org/10.1515/gmj-2018-0017
- Jian, T.A. and Liu, Z.G. (2018) Some Boundedness of Homogeneous Fractional Integrals on Variable Exponent Function Spaces. ACTA Mathematics Science. Chinese Series, 58, 310-320.
- Hammad, N., Humberto, R. and Muhammad, A. (2020) A Note on the Boundedness of Sublinear Operators on Grand Variable Herz Spaces. Journal of Inequalities and Applications, 1, 1-13. https://doi.org/10.1186/s13660-019-2265-6
- Mitsuo, I. (2010) Boundedness of Sublinear Operators on Herz Spaces with Variable Exponent and Application to Wavelet Characterization. Analysis Mathematica, 36, 33-50. https://doi.org/10.1007/s10476-010-0102-8
- Wang, H. and Liao, F. (2020) Boundedness of Singular Integral Operators on Herz-Morrey Spaces with Variable Exponent. Chinese Annals of Mathematics, Series, 41, 99116. https://doi.org/10.1007/s11401-019-0188-7
- Eiichi, N. and Yoshihiro, S. (2012) Hardy Spaces with Variable Exponents and Generalized Campanato Spaces. Journal of Functional Analysis, 262, 3665-3748. https://doi.org/10.1016/j.jfa.2012.01.004
- Muckenhoupt. B. and Wheeden, R.L. (1971) Weighted Norm Inequalities for Singular and Fractional Integrals. Transactions of the American Mathematical Society. 161, 249-258. https://doi.org/10.1090/S0002-9947-1971-0285938-7
- Diening, L., Harjulehto, P., Hst, P. and Ruzicka, M. (2011) Lebesgue and Sobolev Spaces with Variable Exponents. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18363-8