Related papers: Hardy Spaces ($1<p<\infty$) over Lipschitz Domains

For $0<p \leq \infty$, let $H^p$ denote the classical Hardy space of the unit disc. We consider the extremal problem of maximizing the modulus of the $k$th Taylor coefficient of a function $f \in H^p$ which satisfies $\|f\|_{H^p}\leq1$ and…

For $\lambda\ge0$, a $C^2$ function $f$ defined on the unit disk ${{\mathbb D}}$ is said to be $\lambda$-analytic if $D_{\bar{z}}f=0$, where $D_{\bar{z}}$ is the (complex) Dunkl operator given by…

We consider Ces\'aro operator on the Hardy space $H^p(\mathbb{C}_+)$ in the upper half-plane for $1<p<\infty$. In \cite{AS} it was proved that for all $1<p<\infty$ the spectrum of the operator $V=\frac{2(p-1)}{p}C-I$ is located on the unit…

In this paper, we will study the boundedness of intrinsic square functions on the weighted Hardy spaces $H^p(w)$ for $0<p<1$, where $w$ is a Muckenhoupt's weight function. We will also give some intrinsic square function characterizations…

Let \Omega\subset\mathbb{R}^n be a bounded domain with C^\infty boundary. We show that a harmonic function in \Omega that is Lipschitz along a family of curves transversal to b\Omega is Lipschitz in \Omega. The space of Lipschitz functions…

A well known result of C. Cowen states that, for a symbol $\varphi \in L^{\infty }, \; \varphi \equiv \bar{f}+g \;\;(f,g\in H^{2})$, the Toeplitz operator $T_{\varphi }$ acting on the Hardy space of the unit circle is hyponormal if and only…

We study $H^p$ spaces of Dirichlet series, called $\mathcal{H}^p$, for the range $0<p< \infty$. We begin by showing that two natural ways to define $\mathcal{H}^p$ coincide. We then proceed to study some linear space properties of…

The well known result of Bourgain and Kwapie\'n states that the projection $P_{\leq m}$ onto the subspace of the Hilbert space $L^2\left(\Omega^\infty\right)$ spanned by functions dependent on at most $m$ variables is bounded in $L^p$ with…

In this paper we study Hardy spaces $\mathcal{H}^{p,q}(\mathbb{R}^d)$, $0<p,q<\infty$, modeled over amalgam spaces $(L^p,\ell^q)(\mathbb{R}^d)$. We characterize $\mathcal{H}^{p,q}(\mathbb{R}^d)$ by using first order classical Riesz…

In this paper we introduce the atomic Hardy space $\mathcal{H}^1((0,\infty),\gamma_\alpha)$ associated with the non-doubling probability measure $d\gamma_\alpha(x)=\frac{2x^{2\alpha+1}}{\Gamma(\alpha+1)}e^{-x^2}dx$ on $(0,\infty)$, for…

We prove several characterizations of the Hardy spaces for Fourier integral operators $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$, for $1<p<\infty$. First we characterize $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$ in terms of…

A function space, $L^{\theta,\infty)}(\Omega)$, $0 \leq \theta <\infty$, is defined. It is proved that $L^{\theta,\infty)}(\Omega)$ is a Banach space which is a generalization of exponential class. An alternative definition of…

We establish endpoint bounds on a Hardy space $H^1$ for a natural class of multiparameter singular integral operators which do not decay away from the support of rectangular atoms. Hence the usual argument via a Journ\'e-type covering lemma…

The aim of this paper is twofold. On the one hand, we manage to identify Banach-valued Hardy spaces of analytic functions over the disc $\mathbb{D}$ with other classes of Hardy spaces, thus complementing the existing literature on the…

Let ${\mathcal X}$ be an RD-space with $\mu({\mathcal X})=\infty$, which means that ${\mathcal X}$ is a space of homogeneous type in the sense of Coifman and Weiss and its measure has the reverse doubling property. In this paper, we…

Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function satisfying that there exists a constant $p_0\in(0,p_-)$, where $p_-:=\mathop{\mathrm {ess\,inf}}_{x\in \mathbb R^n}p(x)$, such that the Hardy-Littlewood maximal…

Let $p \in (1,\infty)$ and $\Omega \subset \mathbb{R}^N$ be a domain. Let $ A: =(a_{ij}) \in L^{\infty}_{\text{loc}}(\Omega; \mathbb{R}^{N\times N})$ be a symmetric and locally uniformly positive definite matrix. Set $|\xi|_A^2:=…

Let $\mathbb{H}^{n}$ be the Heisenberg group and $Q = 2n+2$. For $1 < q < \infty$, $\gamma > 0$ and an exponent function $p(\cdot)$ on $\mathbb{H}^n$, which satisfy log-H\"older conditions, with $0 < p_{-} \leq p_{+} < \infty$, we introduce…

Let $L=-\Delta+V$ be a Schr\"odinger operator acting on $L^2(\mathbb R^n)$, $n\ge1$, where $V\not\equiv 0$ is a nonnegative locally integrable function on $\mathbb R^n$. In this paper, we first define molecules for weighted Hardy spaces…

Let $\mathscr{H}^2$ denote the Hardy space of Dirichlet series $f(s) = \sum_{n\geq1} a_n n^{-s}$ with square summable coefficients and suppose that $\varphi$ is a symbol generating a composition operator on $\mathscr{H}^2$ by…