The Lebesgue measure is an important concept with applications in the Lebesgue integral, in the axiomatization of probabilities, and in the definion of integral of spaces more general than the euclidian spaces. This essay ...

We give sufficient conditions on variable exponent functions p : Rn → [1,∞) for which the higher-order Riesz transforms, associated with the Ornstein–Uhlenbeck semigroup, are bounded on Lp(·) (Rn, dγ ), where γ denotes the ...

We characterize the power weights ω for which the fractional type operator Tα , β is bounded from Lp(ωp) into Lq(ωq) for 1 < p< n/ (n- (α+ β)) and 1 / q= 1 / p- (n- (α+ β)) / n. If n/ (n- (α+ β)) ≤ p< n/ (n- (α+ β) - 1) + ...

We prove that a generalized Fefferman-Phong type condition on a pair of weights uand v is sufficient for the boundedness of the commutators of potential type operators from Lp(·)_v into Lq(·)_u. We also give an improvement ...

En la presente tesis nos enfocamos en el estudio de algunos operadores integrales, en el contexto de los espacios de Lebesgue con exponente variable. Obtuvimos acotaciones estimaciones de tipo fuerte y de tipo débil para ...

En el Análisis Armónico nos encontramos frecuentemente con el problema de la continuidad, en diferentes contextos, de una amplia gama de operadores que surgen del estudio de la regularidad de soluciones de ecuaciones ...

We prove that a generalized Fefferman–Phong type conditions on a pair of weights u and v is sufficient for the boundedness of the potential type operator from Lv p(.) into Lu q(.). We also obtain an analogous estimates for ...

We characterize the weights for the Stieltjes transform and the Calder´on operator to be bounded on the weighted variable Lebesgue spaces $L_w^{p(cdot)}(0,infty)$, assuming that the exponent function $pp$ is log-H"older ...

In this note we prove that Haar type systems are unconditional basis in the generalized dyadic Hardy space HD 1 in the setting of spaces of homogeneous type. As a consequence, we obtain an alternative proof of the ...