arXiv subjects

Jose Angel Pelaez

Publications and source records attributed to Jose Angel Pelaez.

3 recordsLinked to original sources

arXiv2018

Radial averaging operator acting on Bergman and Lebesgue spaces

It is shown that the radial averaging operator $$ T_ω(f)(z)=\frac{\int_{|z|}^1f\left(s\frac{z}{|z|}\right)ω(s)\,ds}{\widehatω(z)},\quad \widehatω(z)=\int_{|z|}^1ω(s)\,ds, $$ induced by a radial weight $ω$ on the unit disc $\mathbb{D}$, is bounded from the weighted Bergman space $A^p_ν$, where $0 0, $$ are established for arbitrary radial weights $ω$, $ν$ and $η$. Moreover, differences and interrelationships between the cases $A^p_ν\to L^p_ν$, $L^p_ν\to L^p_ν$ and $L^p_ν\to L^{p,\infty}_ν$ are analyzed.

math.CV↗

arXiv2014

Boundedness of the Bergman projection on $L^p$ spaces with exponential weights

Let $v(r)=\exp\left(-\fracα{1-r}\right)$ with $α>0$, and let $\mathbb{D}$ be the unit disc in the complex plane. Denote by $A^p_v$ the subspace of analytic functions of $L^p(\mathbb{D},v)$ and let $P_v$ be the orthogonal projection from $L^2(\mathbb{D},v)$ onto $A^2_v$. In 2004, Dostanic revealed the intriguing fact that $P_v$ is bounded from $L^p(\mathbb{D},v)$ to $A^p_v$ only for $p=2$, and he posed the related problem of identifying the duals of $A^p_v$ for $p\ge 1$, $p\neq 2$. In this paper we propose a solution to this problem by proving that $P_v$ is bounded from $\,L^p(\D,v^{p/2})$ to $A^p_{v^{p/2}}$ whenever $1\le p <\infty$, and, consequently, the dual of $A^p_{v^{p/2}}$ for $p\ge 1$ can be identified with $A^{q}_{v^{q/2}}$, where $1/p+1/q=1$. In addition, we also address a similar question on some classes of weighted Fock spaces.

math.FA↗

arXiv2013

A generalized Hilbert matrix acting on Hardy spaces

If $μ$ is a positive Borel measure on the interval $[0, 1)$, the Hankel matrix $\mathcal H_μ=(μ_{n,k})_{n,k\ge 0}$ with entries $μ_{n,k}=\int_{[0,1)}t^{n+k}\,dμ(t)$ induces formally the operator $$\mathcal{H}_μ(f)(z)=\sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty}μ_{n,k}{a_k}\right)z^n$$ on the space of all analytic functions $f(z)=\sum_{k=0}^\infty a_kz^k$, in the unit disc $\mathbb{D} $. In this paper we describe those measures $μ$ for which $\mathcal{H}_μ$ is a bounded (compact) operator from $H^p$ into $H^q$, $0<p,q<\infty $. We also characterize the measures $μ$ for which $\mathcal H_μ$ lies in the Schatten class $S_p(H^2)$, $1<p<\infty$.

math.FA↗