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Young Women in Harmonic Analysis and PDE
December 2-4, 2016
Edyta Kania (University of Wrocław)
Hardy spaces for Bessel-Schrödinger operators
Let $K_t = exp(-\mathbf{L}t)$ be the semigroup generated by a Bessel-Schrödinger operator on $L^2((0,\infty), x^\alpha dx)$ given by
$$ \mathbf{L}f(x) = -f''(x) - \frac{\alpha}{x} f'(x) + V(x) f(x),$$
where $V\in L^1_{loc}((0,\infty), x^\alpha dx)$ is a non-negative potential and $\alpha>0$. We say that $\,\,\,f\in L^1((0,\infty), x^\alpha dx)$ belongs to Hardy space $\mathcal{H}^1(\mathbf{L})$ if
$$\| \sup_{t>0} |K_t f| \|_{L^1((0,\infty), x^\alpha dx)} <\infty.$$ Under certain assumptions on $V$ and $K_t$ we characterize the space $\mathcal{H}^1(\mathbf{L})$ by atomic decomposition of local type. Moreover, we provide an application of this result for any potential $0\leq V\in L^1_{loc}((0,\infty), x^\alpha dx)$ and for $\alpha\in(0,1)$.
The talk is based on joint work with Marcin Preisner (University of Wrocław).
News
Jessica Fintzen wins Cole Prize
Dr. Regula Krapf receives university teaching award
Prof. Catharina Stroppel joined the North Rhine-Westphalia Academy for Sciences and Arts
Prof. Daniel Huybrechts receives the Compositio Prize for the periode 2017-2019
Prof. Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023
Grants for Mathematics students from Ukraine
Prof. Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society
Prof. Peter Scholze elected as Foreign Member of the Royal Society