Related papers: Two weight inequality for Bergman projection

In this paper, we characterize invertible Toeplitz products on a number of Banach spaces of analytic functions, including weighted Bergman space $L^p_a (\mathbb{B}_n, dv_\gamma)$, the Hardy space $H^p(\partial \mathbb{D})$, and the weighted…

In this work we present a newly developed study of the interpolation of weighted Sobolev spaces by the complex method. We show that in some cases, one can obtain an analogue of the famous Stein-Weiss theorem for weighted $L^{p}$ spaces. We…

In two-dimensional Lipschitz domains, we analyze a Brinkman--Darcy--Forchheimer problem on the weighted spaces $\mathbf{H}_0^1(\omega,\Omega) \times L^2(\omega,\Omega)/\mathbb{R}$, where $\omega$ belongs to the Muckenhoupt class $A_2$.…

In this paper we prove two-weighted norm estimates for higher order commutator of singular integral and fractional type operators between weighted $L^p$ and certain spaces that include Lipschitz, BMO and Morrey spaces. We also give the…

In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_\varphi$ on Bergman type spaces $A_\omega^p $ with double weight $\omega$. Let $X=\{u\in H(D):…

In this paper we investigate the regularity properties of weighted Bergman projections for smoothly bounded pseudo-convex domains of finite type in $\mathbb{C}^{n}$. The main result is obtained for weights equal to a non negative rational…

We show that, on convex polytopes and two or three dimensions, the finite element Stokes projection is stable on weighted spaces $\mathbf{W}^{1,p}_0(\omega,\Omega) \times L^p(\omega,\Omega)$, where the weight belongs to a certain…

We establish necessary and sufficient conditions on a weight pair $(v,w)$ governing the boundedness of the Riesz potential operator $I_{\alpha}$ defined on a homogeneous group $G$ from $L^p_{dec,r}(w, G)$ to $L^q(v, G)$, where…

Let $v,~\omega_1, ~\omega_2$ be weights and $1<p_1, ~p_2<\infty.$ Suppose that $\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}$ and $(\omega_1, \omega_2)\in RH(p_1, p_2).$ For the multisublinear maximal operator $\mathfrak{M}$ in martingale…

We obtain $L^p$ regularity for the Bergman projection on some Reinhardt domains. We start with a bounded initial domain $\Omega$ with some symmetry properties and generate successor domains in higher {dimensions}. We prove: If the Bergman…

If a bounded domain can be covered by the polydisk through a rational proper holomorphic map, then the Bergman projection is $L^p$-bounded for $p$ in a certain range depending on the ramified rational covering. This result can be applied to…

In the paper, we introduce the concept of weight with reasonable growth on a locally compact group $G$. We verify that these weights form a natural class to work with, by examining the most common examples. We proceed with the discussion of…

For $\alpha>0$, the Bargmann projection $P_\alpha$ is the orthogonal projection from $L^2(\gamma_\alpha)$ onto the holomorphic subspace $L^2_{hol}(\gamma_\alpha)$, where $\gamma_\alpha$ is the standard Gaussian probability measure on $\C^n$…

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…

This manuscript addresses Muckenhoupt $A_{p}$ weight theory in connection to Morrey and BMO spaces. It is proved that $\omega$ belongs to Muckenhoupt $A_{p}$ class, if and only if Hardy-Littlewood maximal function $M$ is bounded from…

For a wide range of pairs of mixed norm spaces such that one space is contained in another, we characterize all cases when contractive norm inequalities hold. In particular, this yields such results for many pairs of weighted Bergman…

In this paper, we consider weighted Bergman spaces $\mathcal{B}_{\alpha,p}$ of log-subharmonic functions on the unit sphere. Using the isoperimetric inequality for the spherical metric we prove certain monotonicity property for super-level…

We prove that if a weight is a Bekoll\'{e}-Bonami weight for some $q$ and it satisfies another simple condition that depends on $0 < p < \infty$, then the operator taking a function to its harmonic conjugate is bounded on the harmonic…

We consider sharp inequalities for Bergman spaces of the unit disc, establishing analogues of the inequality in Carleman's proof of the isoperimetric inequality and of Weissler's inequality for dilations. By contractivity and a standard…

In recent work with Berndtsson and Rubinstein, a notion of $L^p$-polarity was introduced, with classical polarity recovered in the limit $p\to\infty$, and $L^1$-polarity closely related to Bergman kernels of tube domains. A Santal\'o…