Harmonic analysis of Riesz-type transforms arising in nonlocal partial differential equations

Abstract

where s ∈ (0, 1) and g is a given function, has been widely studied under different assumptions on the kernel K. In this work, we introduce an operator associated to the above nonlocal equation via Riesz potential. Under assumptions that K is measurable, symmetric and elliptic, we obtain that such an operator is a CalderónZygmund operator