A note on some Endpoint Estimates of Commutators of Fractional Integral Operators

Verrel Rievaldo  Wijaya; Denny Ivanal  Hakim; Marcus Wono  Setya Budhi

doi:10.22342/jims.29.3.1599.322-327

Verrel Rievaldo Wijaya ⁽¹⁾ , Denny Ivanal Hakim ⁽²⁾ , Marcus Wono Setya Budhi ⁽³⁾

(1) Department of Mathematics, Bandung Institute of Technology, Indonesia,

(2) Department of Mathematics, Bandung Institute of Technology, Indonesia,

(3) Department of Mathematics, Bandung Institute of Technology, Indonesia

https://doi.org/10.22342/jims.29.3.1599.322-327

Issue
VOLUME 29 NUMBER 3 (NOVEMBER 2023)

Submitted
December 8, 2023

Published
November 30, 2023

Keywords:

fractional integral operators, commutators, Riesz transform, Lebesgue spaces

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Abstract

It is known that fractional integral operators are not bounded from Lebesgue integrable functions to Lebesgue space for some particular related exponent. Based on some recent results by Schikorra, Spector, and Van Schaftingen, we investigate commutators of fractional integral operators on Lebesgue integrable functions. We establish a weak type estimates for these commutators generated by essentially bounded functions. Under the same assumption, we also prove that the norm of these commutators are dominated by the norm of the Riesz transform.

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References

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Authors

Verrel Rievaldo Wijaya

Department of Mathematics, Bandung Institute of Technology

Denny Ivanal Hakim

Department of Mathematics, Bandung Institute of Technology

dhakim@itb.ac.id (Primary Contact)

Marcus Wono Setya Budhi

Department of Mathematics, Bandung Institute of Technology

Wijaya, V. R. ., Hakim, D. I. ., & Setya Budhi, M. W. . (2023). A note on some Endpoint Estimates of Commutators of Fractional Integral Operators. Journal of the Indonesian Mathematical Society, 29(3), 322–327. https://doi.org/10.22342/jims.29.3.1599.322-327