Related papers: Weighted estimates for the Bergman projection on t…
We obtain sharp weighted estimates for solutions of the equation $\partial$ u = f in a lineally convex domain of finite type. Precisely we obtain estimates in the spaces L p ($\Omega$,$\delta$ $\gamma$), $\delta$ being the distance to the…
In this paper, we investigate a class of domains $\Omega^{n+1}_\gamma =\{(z,w)\in \mathbb{C}^n\times \mathbb{C}: |z|^\gamma < |w| < 1\}$ for $\gamma>0$ that generalizes the Hartogs triangle. We obtain a sharp range of $p$ for the…
We show that on smooth complete Reinhardt domains, weighted Bergman projection operators corresponding to exponentially decaying weights are unbounded on $L^p$ spaces for all $p\not=2$. On the other hand, we also show that the exponentially…
We generalize the Hartogs triangle to a class of bounded Hartogs domains, and we prove that the corresponding Bergman projections are bounded on $L^p$ if and only if $p$ is in the range $(\frac{2n}{n+1},\frac{2n}{n-1})$.
Motivated by the Forelli--Rudin projection theorem we give in this paper a criterion for boundedness of an integral operator on weighted Lebesgue spaces in the interval $(0,1)$. We also calculate the precise norm of this integral operator.…
It is known that the Bergman projection operator maps the space of essentially bounded functions in the unit ball in the d-dimensional complex vector space onto the Bloch space of the unit ball. This paper deals with the various semi-norms…
We obtain ceratin estimates for the reproducing kernels of large weighted Bergman spaces. Applications of these estimates to boundedness of the Bergman projection on $L^p(\D,\omega ^{p/2})$, complex interpolation and duality of weighted…
In this paper, we introduce a dyadic structure on convex domains of finite type via the so-called dyadic flow tents. This dyadic structure allows us to establish weighted norm estimates for the Bergman projection $P$ on such domains with…
We prove some weighted $L_p$ estimates for generalized harmonic extensions in the half-space.
This paper deals with the the norm of the weighted Bergman projection operator $P_\alpha:L^\infty\to \mathcal{B}$ where $\alpha>-1$ and $\mathcal{B}$ is the Bloch space of the unit ball of the complex space $\mathbf{C}^n$. We consider two…
In this paper, we study the norms of multiplication operators acting between weighted Bergman spaces. First, we provide a proof for a norm estimate previously announced in our recent paper \cite{Jin-c}. Second, we establish a sharp norm…
Two-side estimates for two-weighted discrete Hardy-type operators on a tree are obtained. For general weights we prove the discrete analogue of Evans - Harris - Pick theorem (it is a quite simple consequence from their result). It gives the…
The main result of this paper is related to finding two-sided bounds of norm for the adjoint operator $P^{\ast}$ of the Bergman projection $P,$ where $P$ denotes the Bergman projection wich maps $L^{1}(D,d\lambda(z))$ onto the Besov space…
We consider $L^p$-$L^q$ estimates for the spherical harmonic projection operators and obtain sharp bounds on a certain range of $p$, $q$. As an application, we provide a proof of off-diagonal Carleman estimates for the Laplacian, which…
For $1<p<\infty$, we emulate the Bergman projection on Reinhardt domains by using a Banach-space basis of $L^p$-Bergman space. The construction gives an integral kernel generalizing the ($L^2$) Bergman kernel. The operator defined by the…
We give a new proof of the sharp weighted $L^2$ inequality ||T||_{L^2(w)} \leq c [w]_{A_2} where $T$ is the Hilbert transform, a Riesz transform, the Beurling-Ahlfors operator or any operator that can be approximated by Haar shift…
We provide quantitative weighted estimates for the $L^p(w)$ norm of a maximal operator associated to cube skeletons in $\mathbb{R}^n$. The method of proof differs from the usual in the area of weighted inequalities since there are no…
We obtain in this short article the non-asymptotic exact estimations for the norm of (generalized) weighted Hardy-Littlewood average integral operator in the so-called Bilateral Grand Lebesgue Spaces. We also give examples to show the…
Expected duality and approximation properties are shown to fail on Bergman spaces of domains in $\mathbb{C}^n$, via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation…
We provide lower $L^q$ and weak $L^p$-bounds for the localized dyadic maximal operator on $R^n$, when the local $L^1$ and the local $L^p$ norm of the function are given. We actually do that in the more general context of homo- geneous…