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

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

Journal of the Indonesian Mathematical Society
VOLUME 29 NUMBER 3 (NOVEMBER 2023)

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.