Related papers: Pointwise multipliers in Hardy-Orlicz spaces, and …

Following Sarason's classification of the densely defined multiplication operators over the Hardy space, we classify the densely defined multipliers over the Sobolev space, $W^{1,2}[0,1]$. In this paper we find that the collection of such…

To every non-extreme point $b$ of the unit ball of $\hil^\infty$ of the unit disk there corresponds a Pythagorean mate, a bounded outer function $a$ satisfying the equation $|a|^2 + |b|^2 = 1$ on the boundary of the disk. We study…

Consider the second order divergence form elliptic operator $L$ with complex bounded coefficients. In general, the operators related to it (such as Riesz transform or square function) lie beyond the scope of the Calder\'{o}n-Zygmund theory.…

We obtain new results on Fourier multipliers for Dirichlet-Hardy spaces. As a consequence, we establish a Littlewood-Paley type inequality which yields a simple proof that the Dirichlet monomials form a Schauder basis for p>1.

It is well known that a function is in a Bergman space of the unit ball if and only if it satisfies some Hardy-type inequalities. We extend this fact to Bergman-Orlicz spaces. As applications, we obtain Gustavsson-Peetre interpolation of…

Let $\Omega$ be a strongly Lipschitz domain of $\reel^n$. Consider an elliptic second order divergence operator $L$ (including a boundary condition on $\partial\Omega$) and define a Hardy space by imposing the non-tangential maximal…

C. Stockdale, P. Villarroya, and B. Wick introduced the $\epsilon$-maximal operator to prove the Haar multiplier is bounded on the weighted spaces $L^p(w)$ for a class of weights larger than $A_p$. We prove the $\epsilon$-maximal operator…

We characterize the symbols of Hankel operators that ex- tend into bounded operators from the Hardy-Orlicz $H^{\Phi_1} (\mathbb B^n)$ into $H^{\Phi_2} (\mathbb B^n)$ in the unit ball of Cn, in the case where the growth functions $?\Phi_1$…

In this paper we consider Fourier multiplier operators between vector-valued Besov spaces with different integrability exponents $p$ and $q$, which depend on the type $p$ and cotype $q$ of the underlying Banach spaces. In a previous paper…

In this paper we examine the general theory of continuous frame multipliers in Hilbert space. These operators are a generalization of the widely used notion of (discrete) frame multipliers. Well-known examples include Anti-Wick operators,…

Let $\vec{p}\in(0,\,\infty)^n$, $A$ be an expansive dilation on $\mathbb{R}^n$,and $H^{\vec{p}}_A({\mathbb {R}}^n)$ be the anisotropic mixed-norm Hardy space defined via the non-tangential grand maximal function studied by \cite{hlyy20}. In…

We define and prove characterizations of Hardy-Orlicz spaces of conformal densities.

The real and complex interpolation spaces for the classical Hardy spaces $H^1$ and $H^\infty$ were determined in 1983 by P.W. Jones. Due to the analytic constraints the associated Marcinkiewicz decomposition gives rise to a delicate…

We discuss $L^p(\mathbb R^n)$ boundedness for Fourier multiplier operators that satisfy the hypotheses of the H\"ormander multiplier theorem in terms of an optimal condition that relates the distance $|\frac 1p-\frac12|$ to the smoothness…

Let $L$ be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients on $\mathbb{R}^n$ and $X$ a ball quasi-Banach function space on $\mathbb{R}^n$ satisfying some mild assumptions. Denote by…

Let $(X,\mu)$ be a space with a finite measure $\mu$, let $A$ and $B$ be $w^*$-closed subalgebras of $L^{\infty}(\mu)$, and let $C$ and $D$ be closed subspaces of $L^p(\mu)$ ($1<p<\infty$) that are modules over $A$ and $B$, respectively.…

The aim of this article is to give a complete solution to the problem of the bilinear decompositions of the products of some Hardy spaces $H^p(\mathbb{R}^n)$ and their duals in the case when $p<1$ and near to $1$, via wavelets, paraproducts…

We shall investigate the boundedness of the intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces $M^{\Phi,\varphi}_{w}({\mathbb R}^n)$. In all the cases, the conditions for the boundedness are given…

In this paper, we prove the boundedness of multilinear fractional integral operators from products of Hardy spaces associated with ball quasi-Banach function spaces into their corresponding ball quasi-Banach function spaces. As…

Anisotropic generalized Orlicz spaces have been investigated in many recent papers, but the basic assumptions are not as well understood as in the isotropic case. We study the greatest convex minorant of anisotropic $\Phi$-functions and…