Jesús M. Aldaz (Universidad Autónoma de Madrid and ICMAT)

will speak on

Averaging operators in metric measure spaces

Time: 3:00PM
Date: Tue 27th February 2024
Location: E0.32 (beside Pi restaurant) [map]

Further information

Abstract: Let $(X, d)$ be a separable metric space and let $\mu$ be a Borel measure on $X$ which assigns finite measure to bounded Borel sets. Denote by $B (x,r) $ a ball centered at $x$ of radius $r$. Given $g\in L^1(\mu)$, the averaging operators $A_{r, \mu}$ acting on $g$ are defined as follows: fix $r > 0$ and set
\begin{equation}\label{avop}
A_{r , \mu} g(x) := \frac{1}{\mu
(B(x, r))} \int _{B(x, r)} g(y) \ d\mu (y).
\end{equation}
We will discuss when $A_{r , \mu}$ is a bounded operator on $L^1(\mu)$.

(This talk is part of the Analysis series.)

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