Related papers: A note on Hausdorff-Young inequalities in function…

Given a Muckenhoupt weight $w$ and a second order divergence form elliptic operator $L$, we consider different versions of the weighted Hardy space $H^1_L(w)$ defined by conical square functions and non-tangential maximal functions…

We study weighted $(PLB)$-spaces of ultradifferentiable functions defined via a weight function (in the sense of Braun, Meise and Taylor) and a weight system. We characterize when such spaces are ultrabornological in terms of the defining…

The notion of Fourier transform is among the more important tools in analysis, which has been generalized in abstract harmonic analysis to the level of abelian locally compact groups. The aim of this paper is to further generalize the…

A space of entire functions of several complex variables rapidly decreasing on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is majorized with a help of a family of weight functions (not radial in general) is considered…

We provide quantitative weighted weak type estimates for non-integral square functions in the critical case $p=2$ in terms of the $A_p$ and reverse H\"older constants associated to the weight. The method of proof uses a decoupling of the…

We consider weighted banach spaces of holomorphic functions on the upper half plane that are determined by $ \|f\|=\sup_{y>0,-\infty<x<\infty}p(y)|f(x+iy)|<\infty $ for a very large class of weight functions p. We completely solve the…

Let $s\in{\mathbb R}$, $q\in (0,\infty]$, and $\tau\in[0,\infty)$. It is well known that Besov-type spaces $\dot B^{s,\tau}_{p,q}$ with $p\in (0,\infty]$ and Triebel--Lizorkin-type spaces $\dot F^{s,\tau}_{p,q}$ with $p\in (0,\infty)$ when…

Recent work of Lacey-Sawyer-Shen-Uriarte-Tuero and Lacey have established a conjecture of Nazarov-Treil-Volberg, giving a real-variable characterization of the two weight inequality for the Hilbert transform, provided the pair of weights do…

This paper revisits classical fractional Sobolev embedding theorems and the algebra property of the fractional Sobolev space $H^s(\mathbb{R})$ by means of Haar functions and dyadic decompositions. The aim is to provide an alternative,…

This paper is devoted to Hardy type inequalities with remainders for compactly supported smooth functions on open sets in the Euclidean space. We establish new inequalities with weight functions depending on the distance function to the…

In this paper, we introduce and study the Fourier transform of functions which are integrable with respect to a vector measure on a compact group (not necessarily abelian). We also study the Fourier transform of vector measures. We also…

As a corollary to our main result we deduce sharp A_p$ inequalities for T being either the Hilbert transform in dimension d=1, the Beurling transform in dimension d=2, or a Riesz transform in any dimension d\ge 2. For T_{\ast} the maximal…

Fourier transforms of Lorentz invariant functions in Minkowski space, with support on both the timelike and the spacelike domains are performed by means of direct integration. The cases of 1+1 and 1+2 dimensions are worked out in detail,…

In this paper we study the embedding properties for the weighted Sobolev space $H^1_V(\mathbb{R}^N)$ into the Lebesgue weighted space $L^\tau_W(\mathbb{R}^N)$. Here $V$ and $W$ are diverging weight functions. The different behaviour of $V$…

Using elementary arguments based on the Fourier transform we prove that for $1 \leq q < p < \infty$ and $s \geq 0$ with $s > n(1/2-1/p)$, if $f \in L^{q,\infty}(\R^n) \cap \dot{H}^s(\R^n)$ then $f \in L^p(\R^n)$ and there exists a constant…

We introduce a new class $\mathcal{FV}(\Omega,E)$ of spaces of weighted functions on a set $\Omega$ with values in a locally convex Hausdorff space $E$ which covers many classical spaces of vector-valued functions like continuous, smooth,…

We introduce a multi-parameter twisted Hopf algebra associated with a root datum and show that its modified form is isomorphic to Lusztig's modified quantum algebra under certain restrictions on the parameters. By taking various…

A kind of generalized Gelfand pair is introduced via a Banach algebra consisting of bi-invariant functions in a weighted Lebesgue space. The related spherical functions and the Fourier transformation are constructed. The multipliers of the…

Let $\alpha\in\mathbb{R}$, $p\in[1,\infty)$, $q\in(0,\infty]$, $\mathbf{W}$ be a matrix weight, and $A$ be an expansive dilation on $\mathbb{R}^d$. In this paper, the authors firstly investigate and develop some aspects of homogeneous…

The article is devoted to remarkable interrelation between the norm estimates for $k$-plane transforms in weighted and unweighted $L^p$ spaces and geometric integral inequalities for cross-sections of measurable sets in $\mathbb{R}^n$. We…