We characterize those measures μ for which the Hardy-Orlicz (resp. weighted Bergman-Orlicz) space HΨ1 (resp. AΨ1 α ) of the unit ball of CN embeds boundedly or compactly into the Orlicz space LΨ2 ( BN ,μ ) (resp. LΨ2 (BN ,μ)), when the defining functions Ψ1 and Ψ2 are growth functions such that L1 ⊂ LΨ j for i, j ∈ {1,2}, and such that Ψ2/Ψ1 is non-decreasing. We apply our result to the charact...

Let S H f be the Schwarzian derivative of a univalent harmonic function id="M2"> in unit disk id="M3"> D , compatible with finitely generated Fuchsian group id="M4"> G second kind. W...

We consider strongly degenerate parabolic operators of the form \[ \mathcal{L}:=\nabla_X\cdot(A(X,Y,t)\nabla_X)+X\cdot\nabla_Y-\partial_t \] in unbounded domains \Omega=\{(X,Y,t)=(x,x_{m},y,y_{m},t)\in\mathbb R^{m-1}\times\mathbb R\times\mathbb R\mid x_m>\psi(x,y,t)\}. assume that $A=A(X,Y,t)$ is bounded, measurable and uniformly elliptic (as a matrix $\mathbb R^{m}$) concerning $\psi$ $\Omega$...

We prove L estimates for the Walsh model of the maximal bi-Carleson operator defined below. The corresponding estimates for the Fourier model will be obtained in the sequel [20] of this paper.

In this paper we discuss direct and reverse Carleson measures for the de Branges-Rovnyak spaces H (b), mainly when b is a non-extreme point of the unit ball of H.

Let bα(R 1+n + ) be the space of solutions to the parabolic equation ∂tu+ (−△)u = 0 (α ∈ (0, 1]) having finite L(R 1+n + ) norm. We characterize nonnegative Radon measures μ on R + having the property ‖u‖Lq(R1+n + ,μ) . ‖u‖ Ẇ1,p(R + ) , 1 ≤ p ≤ q < ∞, whenever u(t, x) ∈ bα(R 1+n + ) ∩ Ẇ 1.p(R + ). Meanwhile, denoting by v(t, x) the solution of the above equation with Cauchy data v0(x), we chara...

We describe the spectra and essential spectra of Toeplitz operators with piecewise continuous symbols on the Hardy space Hp(Γ, ω) in case 1 < p <∞, Γ is a Carleson Jordan curve and ω is a Muckenhoupt weight in Ap(Γ). Classical results tell us that the essential spectrum of the operator is obtained from the essential range of the symbol by filling in line segments or circular arcs between the en...

In this article, we prove L estimates for a general maximal operator, which extend both the classical Coifman-Meyer [2] and Carleson-Hunt [1], [7] theorems in harmonic analysis.

We characterize the model spaces $K\_\Theta$ in which functions with smooth boundary extensions are dense. It is shown that such approximations possible if and only singular measure associated to inner factor of $\Theta$ concentrated on a countable union Beurling–Carleson sets. In fact, we use duality argument show there exists restriction does not assign positive any set, then even larger clas...