Kyoto Journal of Mathematics

On $n$-dimensional fractional Hardy operators and commutators in variable Herz-type spaces

Abstract

Based on the theory of variable exponents and atomic decomposition, we study the boundedness of $n$-dimensional fractional Hardy operators on variable Herz and Herz-type Hardy spaces, where the three main indices are variable exponents. The corresponding boundedness for the $m$th order commutators generated by the $n$-dimensional fractional Hardy operators and bounded mean oscillation (BMO) function are also considered. We note that, even in the special case of $m=1$, the obtained results are also new.

Article information

Source
Kyoto J. Math., Volume 59, Number 2 (2019), 419-439.

Dates
Revised: 9 March 2017
Accepted: 14 March 2017
First available in Project Euclid: 19 April 2019

https://projecteuclid.org/euclid.kjm/1555660963

Digital Object Identifier
doi:10.1215/21562261-2019-0011

Mathematical Reviews number (MathSciNet)
MR3960300

Zentralblatt MATH identifier
07080111

Citation

Wang, Liwei; Qu, Meng; Tao, Wenyu. On $n$ -dimensional fractional Hardy operators and commutators in variable Herz-type spaces. Kyoto J. Math. 59 (2019), no. 2, 419--439. doi:10.1215/21562261-2019-0011. https://projecteuclid.org/euclid.kjm/1555660963

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