228 research outputs found
Dominación sparse para conmutadores y estimaciones cuantitativas
Dada una funci ́on localmente integrable y un operador lineal T definimos el commutator [b, T ] como
[b, T ]f (x) = b(x)T f (x) − T (bf )(x).
En esta charla presentaremos resultados de dominación sparse para conmutadores y sus iteraciones para los casos en que T es un una integral singular rough, un operador A-Hörmander o un operador de Calderón-Zygmund. Suponiendo adicionalmente que b ∈ BMO o alguna clase análoga mostraremos la versatilidad de las técnicas de dominación sparse para obtener estimaciones cuantitativas.
Esta charla está basada en trabajos conjuntos con A. Lerner, S. Ombrosi, C. P ́erez, L. Roncal y G. Ibañez-Firnkorn.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
A quantitative approach to weighted Carleson Condition
Quantitative versions of weighted estimates obtained by F. Ruiz and J.L.
Torrea in the 80's for the operator are obtained. As a consequence, some sufficient conditions for the
boundedness of in the two weight setting in the spirit of the
results obtained by C. P\'erez and E. Rela and very recently by M.T. Lacey and
S. Spencer for the Hardy-Littlewood maximal operator are derived. As a
byproduct some new quantitative estimates for the Poisson integral are
obtained
On pointwise and weighted estimates for commutators of Calder\'on-Zygmund operators
In recent years, it has been well understood that a Calder\'on-Zygmund
operator is pointwise controlled by a finite number of dyadic operators of
a very simple structure (called the sparse operators). We obtain a similar
pointwise estimate for the commutator with a locally integrable
function . This result is applied into two directions. If , we
improve several weighted weak type bounds for . If belongs to the
weighted , we obtain a quantitative form of the two-weighted bound for
due to Bloom-Holmes-Lacey-Wick.Comment: V3: Lemma 5.1 is corrected. We would like to thank Irina Holmes for
pointing out an error in the previous versio
- …