Do you want to publish a course? Click here

Harmonic conjugates on Bergman spaces induced by doubling weights

129   0   0.0 ( 0 )
 Added by Jose Angel Pelaez
 Publication date 2019
  fields
and research's language is English




Ask ChatGPT about the research

A radial weight $omega$ belongs to the class $widehat{mathcal{D}}$ if there exists $C=C(omega)ge 1$ such that $int_r^1 omega(s),dsle Cint_{frac{1+r}{2}}^1omega(s),ds$ for all $0le r<1$. Write $omegaincheck{mathcal{D}}$ if there exist constants $K=K(omega)>1$ and $C=C(omega)>1$ such that $widehat{omega}(r)ge Cwidehat{omega}left(1-frac{1-r}{K}right)$ for all $0le r<1$. In a recent paper, we have recently prove that these classes of radial weights arise naturally in the operator theory of Bergman spaces induced by radial weights. Classical results by Hardy and Littlewood, and Shields and Williams, show that the weighted Bergman space of harmonic functions is not closed by harmonic conjugation if $omegainwidehat{mathcal{D}}setminus check{mathcal{D}}$ and $0<ple 1$. In this paper we establish sharp estimates for the norm of the analytic Bergman space $A^p_omega$, with $omegainwidehat{mathcal{D}}setminus check{mathcal{D}}$ and $0<p<infty$, in terms of quantities depending on the real part of the function. It is also shown that these quantities result equivalent norms for certain classes of radial weights.



rate research

Read More

Bounded and compact differences of two composition operators acting from the weighted Bergman space $A^p_omega$ to the Lebesgue space $L^q_ u$, where $0<q<p<infty$ and $omega$ belongs to the class $mathcal{D}$ of radial weights satisfying a two-sided doubling condition, are characterized. On the way to the proofs a new description of $q$-Carleson measures for $A^p_omega$, with $p>q$ and $omegainmathcal{D}$, involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of $q$-Carleson measures for the classical weighted Bergman space $A^p_alpha$ with $-1<alpha<infty$ to the setting of doubling weights. The case $omegainwidehat{mathcal{D}}$ is also briefly discussed and an open problem concerning this case is posed.
117 - Atte Reijonen 2019
Let $1le p<infty$, $0<q<infty$ and $ u$ be a two-sided doubling weight satisfying $$sup_{0le r<1}frac{(1-r)^q}{int_r^1 u(t),dt}int_0^rfrac{ u(s)}{(1-s)^q},ds<infty.$$ The weighted Besov space $mathcal{B}_{ u}^{p,q}$ consists of those $fin H^p$ such that $$int_0^1 left(int_{0}^{2pi} |f(re^{itheta})|^p,dthetaright)^{q/p} u(r),dr<infty.$$ Our main result gives a characterization for $fin mathcal{B}_{ u}^{p,q}$ depending only on $|f|$, $p$, $q$ and $ u$. As a consequence of the main result and inner-outer factorization, we obtain several interesting by-products. In particular, we show the following modification of a classical factorization by F. and R. Nevanlinna: If $fin mathcal{B}_{ u}^{p,q}$, then there exist $f_1,f_2in mathcal{B}_{ u}^{p,q} cap H^infty$ such that $f=f_1/f_2$. In addition, we give a sufficient and necessary condition guaranteeing that the product of $fin H^p$ and an inner function belongs to $mathcal{B}_{ u}^{p,q}$. Applying this result, we make some observations on zero sets of $mathcal{B}_{ u}^{p,p}$.
92 - Beno^it F. Sehba 2017
We prove some characterizations of Schatten class Toeplitz operators on Bergman spaces of tube domains over symmetric cones for small exponents.
88 - Blake J. Boudreaux 2018
We give a proof that every space of weighted square-integrable holomorphic functions admits an equivalent weight whose Bergman kernel has zeroes. Here the weights are equivalent in the sense that they determine the same space of holomorphic functions. Additionally, a family of radial weights in $L^1(mathbb{C})$ whose associated Bergman kernels have infinitely many zeroes is exhibited.
We establish a weighted inequality for the Bergman projection with matrix weights for a class of pseudoconvex domains. We extend a result of Aleman-Constantin and obtain the following estimate for the weighted norm of $P$: [|P|_{L^2(Omega,W)}leq C(mathcal B_2(W))^{{2}}.] Here $mathcal B_2(W)$ is the Bekolle-Bonami constant for the matrix weight $W$ and $C$ is a constant that is independent of the weight $W$ but depends upon the dimension and the domain.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا