Affiliation:
1. Department of Mathematics , Quaid-I-Azam University , Islamabad 45320 , Pakistan
2. Department of Mathematics , Capital University Of Science and Technology , Islamabad , Pakistan
Abstract
Abstract
The aim of this paper is to obtain the boundedness of commutators of Hardy operators with rough kernels on grand variable Herz spaces
K
˙
q
(
⋅
)
a
(
⋅
)
,
u
,
θ
(
ℝ
n
)
{\dot{K}^{a(\,\cdot\,),u,\theta}_{q(\,\cdot\,)}(\mathbb{R}^{n})}
by applying some properties of variable exponent. Moreover, by using the idea of grand variable Herz–Morrey spaces,
we will prove the boundedness of Hardy operators on these spaces.
Subject
Applied Mathematics,General Mathematics
Reference23 articles.
1. M. Asim, A. Hussain and N. Sarfraz,
Weighted variable Morrey–Herz estimates for fractional Hardy operators,
J. Inequal. Appl. 2022 (2022), Paper No. 2.
2. S. Bashir, B. Sultan, A. Hussain, A. Khan and T. Abdeljawad,
A note on the boundedness of Hardy operators in grand Herz spaces with variable exponent,
AIMS Math. 8 (2023), no. 9, 22178–22191.
3. D. V. Cruz-Uribe and A. Fiorenza,
Variable Lebesgue Spaces, Foundations and Harmonic Analysis,
Appl. Numer. Harmon. Anal.,
Birkhäuser, Heidelberg, 2013.
4. Z. Fu, L. Grafakos, S. Lu and F. Zhao,
Sharp bounds for m-linear Hardy and Hilbert operators,
Houston J. Math. 38 (2012), no. 1, 225–244.
5. Z.-W. Fu, Z.-G. Liu, S.-Z. Lu and H.-B. Wang,
Characterization for commutators of n-dimensional fractional Hardy operators,
Sci. China Ser. A 50 (2007), no. 10, 1418–1426.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献