Weighted grand Lebesgue spaces with mixed-norms and integral operators
- Authors: Kokilashvili V.M.1
-
Affiliations:
- A. Razmadze Mathematical Institute of I. Javakhishvili, Tbilisi State University
- Issue: Vol 489, No 4 (2019)
- Pages: 344-346
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/18681
- DOI: https://doi.org/10.31857/S0869-56524894344-346
- ID: 18681
Cite item
Full Text
Abstract
In this paper, the weighted grand Lebesgue spaces with mixed-norms are introduced and boundedness criteria in these spaces of strong maximal functions and Riesz transforms are presented.
About the authors
V. M. Kokilashvili
A. Razmadze Mathematical Institute of I. Javakhishvili, Tbilisi State University
Author for correspondence.
Email: vakhtangkokilashvili@yahoo.com
Georgia, 1, M. Aleksidze str., Tbilisi, 380093
References
- Benedek A., Panzone R. // Duke Math. J. 1961. V. 28. P. 301-324.
- Iwaniec T., Sbordone C. // Arch. Rational Mech. Anal. 1992. V. 119. № 2. P. 129-143.
- Greco L., Iwaniec T., Sbordone C. // Manuscripta Math. 1997. V. 92. № 2. P. 249-258.
- Fiorenza A., Gupta B., Jain P. // Studia Math. 2008. V. 188. № 2. P. 123-133.
- Kokilashvili V., Meskhi A. // Georgian Math. J. 2009. V. 16. № 3. P. 547-551.
- Fiorenza A., Kokilashvili V. // Ann. Funct. Anal. 2018. V. 9. № 3. P. 413-425.
- Meskhi A. // J. Math. Sci. N.Y. 2011. V. 178. № 6. P. 622-636.
- Capone C., Formica M.R., Giova R. // Nonlinear Anal. 2013. V. 85. P. 125-131. Zbl 1286.46030.MR3040353. doi: 10.1016/j.na.2013.02.021.414.
- Anatriello G., Fiorenza A. // J. of Math. Analysis and Appl. 2015. V. 422. № 2. P. 783-797.
- Anatriello G., Formica M.R. // Ricerche di Mathematica. 2016. V. 65. № 1. P. 221-233.
- Кокилашвили В.М., Месхи А.Н. // Тр. МИАН. 2016. Т. 293. С. 167-192.
- Samko S.G., Umarkhadzhiev S.M. // Azerb. J. Math. 2011. V. 1. № 1. P. 67-84.
- Kokilashvili V., Meskhi A., Rafeiro H., Samko S. Integral Operators in Non-Standard Function Spaces. II: Variable Exponent Holder, Morrey-Campanato and Grand Spaces // Oper. Theory Adv. Appl. 2016. V. 249. Birkhauser, Cham. Zbl 1367.47004. MR3559401. doi: 10.1007/978-3-319-21018-6.1.414.