Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 913-929

CERTAIN FRACTIONAL TYPE OPERATORS WITH HÖRMANDER CONDITIONS

Gonzalo H. Ibañez Firnkorn and María Silvina Riveros

Universidad Nacional de Cördoba, FaMAF, CIEM (CONICET)
5000 Cördoba, Argentina; gibanez 'at' famaf.unc.edu.ar

Universidad Nacional de Cördoba, FaMAF, CIEM (CONICET)
5000 Cördoba, Argentina; sriveros 'at' famaf.unc.edu.ar

Abstract. In this paper we study fractional type operators with more than one kernel, defined by

T_α,mf(x) = ∫_Rk₁(x – A₁y)k₂(x – A₂y) ··· k_m(x – A_my)f(y) dy,

where, for 1 ≤ i ≤ m, each k_i satisfies a fractional size condition and generalized fractional Hörmander condition, and A_i are invertibles matrices. We obtain weighted Coifman type estimates, strong and weak type inequalities and BMO estimates for this operator. We also present some examples different from those in the literature.

2010 Mathematics Subject Classification: Primary 42B20, 42B25.

Key words: Fractional operators, Hörmander's condition of Young type, weights inequalities.

Reference to this article: G. H. Ibañez Firnkorn and M. S. Riveros: Certain fractional type operators with Hörmander conditions. Ann. Acad. Sci. Fenn. Math. 43 (2018), 913-929.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4353