Certain fractional type operators with Hörmander conditions

G. IBAÑEZ FIRKORN, M.S. RIVEROS

Porto Alegre

Congreso; ICM 2018 Satellite Conference in Harmonic Analysis; 2018

ICM

We study fractional type operators with more than one kernel, definedbyTα,mf(x) = \int _Rn k1(x − A1y)k2(x − A2y). . . km(x − Amy)f(y)dy,where, for 1 ≤ i ≤ m, each ki satisfies a fractional size condition and generalizedfractional Hörmander condition, and Ai are invertibles matrices. We obtain weightedCoifman type estimates, strong and weak type inequalities and BMO estimates forthis operator. We also present some examples different from those in the literature.This work ?Certain fractional type operators with Hörmander conditions? is incollaboration with Lic. Gonzalo H. Ibañez-Firnkorn and has been accepted in AnnalesAcademiae Scientiarum Fennicae Mathematica (03-2018).