Related papers: Integral means of derivatives of univalent functio…

We give a~new proof of the known criteria for the inequality \begin{equation*} \left(\int_{0}^{\infty}\left(\int_{0}^{t}f\right)^{q}w(t)\,dt\right)^{\frac{1}{q}} \leq C \left(\int_{0}^{\infty}f^{p}v\right)^{\frac{1}{p}}. \end{equation*} The…

We study the mean-value harmonic functions on open subsets of $\mathbb{R}^n$ equipped with weighted Lebesgue measures and norm induced metrics. Our main result is a necessary condition saying that all such functions solve a certain…

Let $\vec{p}\in(0,\infty)^n$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. In this article, via the non-tangential grand maximal function, the authors first introduce the anisotropic mixed-norm Hardy spaces…

We show topological genericity for the set of functions in the space X, where X denotes the intersection of the Hardy spaces H^p with p<1, on the open unit disc such that the sequence of Taylor coefficients of the function and of all…

Let $p\in(0,1]$, $q\in(0,\infty]$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. The authors introduce the anisotropic Hardy-Lorentz space $H^{p,q}_A(\mathbb{R}^n)$ associated with $A$ via the non-tangential grand maximal function…

This article studies the Fourier spectrum characterization of functions in the Clifford algebra-valued Hardy spaces $H^p(\mathbf R^{n+1}_+), 1\leq p\leq \infty.$ Namely, for $f\in L^p(\mathbf R^n)$, Clifford algebra-valued, $f$ is further…

In this paper, we show the equivalence between the boundedness of the Riesz transform $d\Delta^{-1/2}$ on $L^p$, $p\in (2,p_0)$, and the equality $H^p=L^p$, $p\in(2,p_0)$, in the class of manifold whose measure is doubling and for which the…

We define Hardy spaces $H^p$, $0<p<\infty$, for quasiconformal mappings on the Kor\'{a}nyi unit ball $B$ in the first Heisenberg group $\mathbb{H}^1$. Our definition is stated in terms of the Heisenberg polar coordinates introduced by…

Let $f$ be a positive multiplicative function and let $k\geq 2$ be an integer. We prove that if the prime values $f(p)$ converge to $1$ sufficiently slowly as $p\rightarrow +\infty$, in the sense that $\sum_{p}|f(p)-1|=\infty$, there exists…

Let $L$ be a one-to-one operator of type $\omega$ in $L^2(\mathbb{R}^n)$, with $\omega\in[0,\,\pi/2)$, which has a bounded holomorphic functional calculus and satisfies the Davies-Gaffney estimates. Let $p(\cdot):\ \mathbb{R}^n\to(0,\,1]$…

We study, for $1 \leq p \leq \infty$, the Hardy space $\bm{h}_e^p(\B)$, the elastic analogue of the classical Hardy spaces of harmonic functions in the unit ball of $\mathbb{R}^3$. The space consists of vector-field solutions of the Lam\'e…

Let $H$ be a Hilbert space that can be embedded as a dense subspace of a Banach space $X$ such that the norm of the embedding is equal to $1$. We consider the following statements for a nonzero vector $\varphi$ in $H$: (A) $\|\varphi\|_X =…

Let $L$ be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients and $(p_-(L),\, p_+(L))$ be the maximal interval of exponents $q\in[1,\,\infty]$ such that the semigroup…

A range of Hardy-like spaces of ordinary Dirichlet series, called the Dirichlet-Hardy spaces $\Hp^p$, $p \geq 1$, have been the focus of increasing interest among researchers following a paper of Hedenmalm, Lindqvist and Seip in Duke Math.…

We consider normalized univalent functions with prescribed second Taylor coefficient $a_2$. For convex functions $f$ we study the Hardy spaces to which $f$ and $f'$ belong, refining in particular on a theorem of Eenigenburg and Keogh, and…

In this paper we investigate continuity properties of functions $f:\mathbb{R}_+\to\mathbb{R}_+$ that satisfy the $(p,q)$-Jensen convexity inequality $$ f\big(H_p(x,y)\big)\leq H_q(f(x),f(y)) \qquad(x,y>0), $$ where $H_p$ stands for the…

We study linear extremal problems in the Bergman space $A^p$ of the unit disc, where $1 < p < \infty$. Given a functional on the dual space of $A^p$ with representing kernel $k \in A^q$, where $1/p + 1/q = 1$, we show that if $q \le q_1 <…

Hardy's inequality on $H^p$ spaces, $p\in(0,1]$, in the context of orthogonal expansions is investigated for general basis on a subset of $\mathbb{R}^d$ with Lebesgue measure. The obtained result is applied to various Hermite, Laguerre, and…

In this work we study the vector-valued Hardy spaces H p (D; F) (1 \leq p \leq \infty) and their relationship with RNP, ARNP and the UMDP properties. By following the approach of Taylor in the scalar-valued case, we prove that, when F and F…

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…