Related papers: Function spaces for decoupling
Let $L$ be the generator of an analytic semigroup whose kernels satisfy Gaussian upper bounds and H\"older's continuity. Also assume that $L$ has a bounded holomorphic functional calculus on $L^2(\mathbb{R}^n)$. In this paper, we construct…
The class of Banach spaces $(L^{q},L^{p}) ^{\alpha}(X,d,\mu)$, $1\leq q\leq \alpha \leq p\leq \infty ,$ introduced in \cite{F1} in connection with the study of the continuity of the fractional maximal operator of Hardy-Littlewood and of the…
Let $X$ be a metric space with a doubling measure. Let $L$ be a nonnegative self-adjoint operator acting on $L^2(X)$, hence $L$ generates an analytic semigroup $e^{-tL}$. Assume that the kernels $p_t(x,y)$ of $e^{-tL}$ satisfy Gaussian…
Bifractional displacement operators, are introduced by performing two fractional Fourier transforms on displacement operators. They are shown to be special cases of elements of the group G, that contains both displacements and squeezing…
We study discrete harmonic analysis associated with ultraspherical orthogonal functions. We establish weighted l^p-boundedness properties of maximal operators and Littlewood-Paley g-functions defined by Poisson and heat semigroups generated…
We consider several problems at or beyond endpoint in harmonic analysis. The solutions of these problems are related to the estimates of some classes of sublinear operators. To do this, we introduce some new functions spaces…
We use the classical Fourier analysis to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained…
We establish exact conditions for non triviality of all subspaces of the standard Hardy space in the upper half plane, that consist of character automorphic functions with respect to the action of a discrete subgroup of $SL_2(\mathbb R)$.…
We obtain Fourier inequalities in the weighted $L_p$ spaces for any $1<p<\infty$ involving the Hardy-Ces\`aro and Hardy-Bellman operators. We extend these results to product Hardy spaces for $p\le 1$. Moreover, boundedness of the…
In this paper, we show that the expansions of functions from $L^p$-Paley-Wiener type spaces in terms of the prolate spheroidal wave functions converge almost everywhere for $1<p<\infty$, even in the cases when they might not converge in…
In this work, we introduce a new family of functions spaces, the weighted fractional Sobolev spaces $X^{s,p}_{0,w}(\Omega)$, where $w$ is a weight in the Muckenhoupt class $A_p$. This space is a natural extension of the fractional Sobolev…
We introduce truncated Besov and Triebel--Lizorkin function spaces and investigate their main properties: embeddings, interpolation, duality, lifting, traces. These new scales allow us to improve several known results in functional analysis…
In this paper we solve the following problems: (i) find two differential operators P and Q satisfying [P,Q]=P, where P flows according to the KP hierarchy \partial P/\partial t_n = [(P^{n/p})_+,P], with p := \ord P\ge 2; (ii) find a matrix…
We establish a Sobolev-type inequality in Lorentz spaces for $\mathcal{L}$-superharmonic functions \[ \|u\|_{L^{\frac{nq}{n-\alpha q},t}(\mathbb{R}^n)} \leq c \left\| \frac{u(x) - u(y)}{|x-y|^{\frac{n}{q}+\alpha}}…
In this article we present formulae for q-integration on quantum spaces which could be of particular importance in physics, i.e. q-deformed Minkowski space and q-deformed Euclidean space in 3 or 4 dimensions. Furthermore, our formulae can…
We introduce floating bodies for convex, not necessarily bounded subsets of $\mathbb{R}^n$. This allows us to define floating functions for convex and log concave functions and log concave measures. We establish the asymptotic behavior of…
We develop an $L^p(\mathbb{R}^n)$-functional calculus appropriated for interpreting "non-classical symbols" of the form $a(-\Delta)$, and for proving existence in $L^q(\mathbb{R}^n)$, some $q > p$, of solutions to nonlinear…
In this paper, we extend the fractional Sobolev spaces with variable exponents $W^{s,p(x,y)}$ to include the general fractional case $W^{K,p(x,y)}$, where $p$ is a variable exponent, $s\in (0,1)$ and $K$ is a suitable kernel. We are…
Given a charge and current distribution with compact support, the associated potentials and fields are generally not integrable in the classical sense. However, it is convenient to be able to define their Fourier transform in order to…
In this paper, we carry on with the study of the Hardy-Amalgam spaces $\mathcal{H}_{\mathrm{loc}}^{(q,p)}$ spaces introduced in \cite{AbFt}. We investigate their dual spaces and establish some results of boundedness of pseudo-differential…