## Optimal exponents in weighted estimatesAdd to your list(s) Download to your calendar using vCal - Teresa Luque (Universidad de Sevilla, Spain)
- Wednesday 04 December 2013, 16:00-17:00
- Room R17/18, Watson building.
If you have a question about this talk, please contact José Cañizo. We are interested in proving the optimality of weighted inequalities of the form:
\begin{align}\label{optimal}
\|Tf\| ^{p$ norm $\|T\|_{L}p(\mathbb{R}^n)}$ as $p$ goes to $1$ and $+\infty$. By combining these results with known weighted inequalities, we derive the sharpness of this exponent $\beta$, without building any specific example, for maximal, Calder\’on—Zygmund and fractional integral operators. The main underlying idea of this result comes from extrapolation theory and the Rubio de Francia algorithm.In the second part, we focus on the case where $T$ is the strong maximal function and $w$ is a \emph{strong}-$A_p$ weight. Although for this operator no such quantitative estimates are currently known, we describe some partial results we have obtained. This talk is part of the Analysis Seminar series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
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