Related papers: Carleson measures and $H^{p}$ interpolating sequen…

For $p\in(0,1),$ let $Q_p$ spaces be the space of all analytic functions on the unit disk $\mathbb{D}$ such that $|f'(z) | ^2 (1-| z| ^2)^p dA(z)$ is a $p$ - Carleson measure. In this paper, we prove that the Wolff's Ideal Theorem on…

We prove in a direct fashion that a multidimensional probability measure is determinate if the higher dimensional analogue of Carleman's condition is satisfied. In that case, the polynomials, as well as certain proper subspaces of the…

We characterize interpolating sequences for pairs of reproducing kernels $(s, \ell)$, where $s$ is a complete Pick factor of $\ell.$ This answers a question of Aleman, Hartz, McCarthy and Richter.

Ingrid Carbone introduced the notion of so-called LS-sequences of points, which are obtained by a generalization of Kakutani's interval splitting procedure. Under an appropriate choice of the parameters $L$ and $S$, such sequences have low…

We consider the Fock-Sobolev space $F^{p,m}$ consisting of entire functions $f$ such that $f^{(m)}$, the $m$-th order derivative of $f$, is in the Fock space $F^p$. We show that an entire function $f$ is in $F^{p,m}$ if and only if the…

We prove that $W^{1}_{p}$ is an interpolation space between $W^{1}_{p_{1}}$ and $W^{1}_{p_{2}}$ for $p>q_{0}$ and $1\leq p_{1}<p<p_{2}\leq \infty$ on some classes of manifolds and general metric spaces, where $q_{0}$ depends on our…

Suppose $\mu$ be a Beltrami coefficient on the unit disk, which is compatible with a convex co-compact Fuchsian group $G$ of the second kind. In this paper we show that if $\displaystyle\frac{|\mu|^{2}}{1-|z|^{2}}dxdy $ satisfies the…

It is shown that every Banach space either contains $\ell ^1$ or it has an infinite dimensional closed subspace which is a quotient of a H.I. Banach space.Further on, $L^p(\lambda )$, $1<p<\infty $, is a quotient of a H.I Banach space.

We give a necessary and sufficient condition for a measure $\mu$ in the closed unit disk to be a reverse Carleson measure for Hardy spaces. This extends a previous result of Lef\'evre, Li, Queff\'elec and Rodr\'{\i}guez-Piazza \cite{LLQR}.…

Let $N$ be the Heisenberg group. We consider left-invariant multiplicity free subspaces of $L^2(N)$. We prove a necessary and sufficient density condition in order that such subspaces possess the interpolation property with respect to a…

We prove that the generalized Carleson operator $C_d$ with polynomial phase function is of strong type $(p,r)$, $1<r<p<\infty$; this yields a positive answer in the $1<p<2$ case to a conjecture of Stein which asserts that for $1<p<\infty$…

We characterize simply interpolating sequences (also known as onto interpolating sequences) for complete Pick spaces. We show that a sequence is simply interpolating if and only if it is strongly separated. This answers a question of Agler…

We introduce a scale of weighted Carleson norms, which depend on an integrability parameter p, where p=2 corresponds to the classical Carleson measure condition. Relations between the weighed BMO norm of a vector-valued function f:R->X, and…

In this paper, we show that if the bounded solutions to the parabolic Dirichlet problem on a Lipshitz-$\left[1,\frac{1}{2}\right]$ domain obey a Carleson measure estimate, then the corresponding parabolic measure on the boundary will belong…

We prove that, for every $\alpha > -1$, the pull-back measure $\phi ({\cal A}_\alpha)$ of the measure $d{\cal A}_\alpha (z) = (\alpha + 1) (1 - |z|^2)^\alpha \, d{\cal A} (z)$, where ${\cal A}$ is the normalized area measure on the unit…

Let $K\subset R^n$ be a compact basic semi-algebraic set. We provide a necessary and sufficient condition (with no a priori bounding parameter) for a real sequence $y=(y_\alpha)$, $\alpha\in N^n$, to have a finite representing Borel measure…

It is well known from a result by Shapiro-Shields that in the Hardy spaces, a sequence of reproducing kernels is uniformly minimal if and only if it is an unconditional basis in its span. This property which can be reformulated in terms of…

We define a scale of L^q Carleson norms, all of which characterize the membership of a function in BMO. The phenomenon is analogous to the John-Nirenberg inequality, but on the level of Carleson measures. The classical Carleson condition…

Coifman--Meyer multipliers represent a very important class of bi-linear singular operators, which were extensively studied and generalized. They have a natural multi-parameter counterpart. Decomposition of those operators into…

In this dissertation, it is first shown that, when the radial basis function is a $p$-norm and $1 < p < 2$, interpolation is always possible when the points are all different and there are at least two of them. We then show that…