Kyoto Journal of Mathematics

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

Liwei Wang, Meng Qu, and Wenyu Tao

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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 mth 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
Received: 15 November 2016
Revised: 9 March 2017
Accepted: 14 March 2017
First available in Project Euclid: 19 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1555660963

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

Mathematical Reviews number (MathSciNet)
MR3960300

Zentralblatt MATH identifier
07080111

Subjects
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 42B35: Function spaces arising in harmonic analysis

Keywords
Herz spaces Herz-type Hardy spaces variable exponents fractional Hardy operators commutators

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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