Related papers: Factorization in mixed norm Hardy and BMO spaces

In this paper, we study multilinear Fourier multiplier operators on Hardy spaces. In particular, we prove that the multilinear Fourier multiplier operator of H\"ormander type is bounded from $H^{p_1} \times \cdots \times H^{p_m}$ to $H^p$…

Let $n$ be a positive integer. Let $\mathbf U$ be the unit disk, $p\ge 1$ and let $h^p(\mathbf U)$ be the Hardy space of harmonic functions. Kresin and Maz'ya in a recent paper found the representation for the function $H_{n,p}(z)$ in the…

Let $0<p<\infty$ and $0\leq q<\infty$. For each $f$ in the weighted Hardy space $H_{p, q}$,\ we show that $d\|f_r\|_{p,q}^p/dr$ grows at most like $o(1/1- r)$ as $r\rightarrow 1$.

We present an extension of the Hardy--Littlewood inequality for multilinear forms. More precisely, let $\mathbb{K}$ be the real or complex scalar field and $m,k$ be positive integers with $m\geq k\,$ and $n_{1},\dots ,n_{k}$ be positive…

A classical observation of Riesz says that truncations of a general $\sum_{n=0}^\infty a_n z^n$ in the Hardy space $H^1$ do not converge in $H^1$. A substitute positive result is proved: these partial sums always converge in the Bergman…

Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function satisfying the globally log-H\"older continuous condition. In this article, the authors first obtain a decomposition for any distribution of the variable weak Hardy…

The purpose of this paper is to introduce and investigate some basic properties of mixed homogeneous Herz-Hardy spaces $H\dot{K}_{\vec{p}}^{\alpha, q}(\mathbb{R}^n)$ and mixed non-homogeneous Herz-Hardy spaces $HK_{\vec{p}}^{\alpha,…

Many fundamental problems in data mining can be reduced to one or more NP-hard combinatorial optimization problems. Recent advances in novel technologies such as quantum and quantum-inspired hardware promise a substantial speedup for…

We give an explicit construction of Haar functions associated to a system of dyadic cubes in a geometrically doubling quasi-metric space equipped with a positive Borel measure, and show that these Haar functions form a basis for $L^p$. Next…

We establish a complete theory of the flag Hardy space on the Heisenberg group $\mathbb H^{n}$ with characterisations via atomic decompositions, area functions, square functions, maximal functions and singular integrals. We introduce…

G. Ricotta and E. Royer (2018) have recently proved that the polygonal paths joining the partial sums of the normalized classical Kloosterman sums $S(a,b;p^n)/p^(n/2) converge in law in the Banach space of complex-valued continuous function…

We study metrically projective and metrically free matricially normed spaces. We describe these spaces in terms of a special space $\widehat M_n$, the space of $n\times n$ matrices, endowed with a special matrix-norm. We show that…

One can define Fourier multipliers on a Banach function space by using the direct and inverse Fourier transforms on $L^2(\mathbb{R}^n)$ or by using the direct Fourier transform on $S(\mathbb{R}^n)$ and the inverse one on $S'(\mathbb{R}^n)$.…

Let $H$ be a Hardy field (a field consisting of germs of real-valued functions at infinity that is closed under differentiation) and let $f \in H$ be a subpolynomial function. Let $\mathcal{P} = \{2, 3, 5, 7, \dots \}$ be the (naturally…

G. Andrews proved that if $n$ is a prime number then the coefficients $a_k$ and $a_{k+n}$ of the product $(q,q)_\infty/(q^n,q^n)_\infty=\sum_k a_kq^k$ have the same sign, see [A1]. We generalize this result in several directions. Our…

For $1<p< \infty$, we show that the Rosenthal $X_{p,w}$ spaces and the Bourgain-Rosenthal-Schechtman $R_{\omega}^{p}$ space have the factorization property and the primary factorization property.

Let $p(\cdot)$ be a measurable function defined on a probability space satisfying $0<p_-:={\rm ess}\inf_{x\in \Omega}p(x)\leq {\rm ess}\sup_{x\in\Omega}p(x)=:p_+<\infty$. We investigate five types of martingale Hardy spaces $H_{p(\cdot)}$…

The mixed principal eigenvalue of $p\,$-Laplacian (equivalently, the optimal constant of weighted Hardy inequality in $L^p$ space) is studied in this paper. Several variational formulas for the eigenvalue are presented. As applications of…

We complete the different cases remaining in the estimation of the essential norm of a weighted composition operator acting between the Hardy spaces $H^p$ and $H^q$ for $1\leq p,q\leq\infty.$ In particular we give some estimates for the…

Let $1\le p<\infty$, $0<q<\infty$ and $\nu$ be a two-sided doubling weight satisfying $$\sup_{0\le r<1}\frac{(1-r)^q}{\int_r^1\nu(t)\,dt}\int_0^r\frac{\nu(s)}{(1-s)^q}\,ds<\infty.$$ The weighted Besov space $\mathcal{B}_{\nu}^{p,q}$…