A note on some Endpoint Estimates of Commutators of Fractional Integral Operators
Verrel Rievaldo Wijaya, Denny Ivanal Hakim (*), Marcus Wono Setya Budhi

Department of Mathematics, Bandung Institute of Technology, Bandung 40132, Indonesia
*dhakim[at]math.itb.ac.id

Abstract

It is known that fractional integral operators are not bounded from Lebesgue integrable functions to Lebesgue space with related exponents. 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.

Keywords: fractional integral operators, commutators, Riesz transform, boundedness

Topic: MATHEMATICS AND STATISTICS