Related papers: Boundedness of Bilinear Bessel Potentials

We establish L^p bounds on L^2 normalized spectral clusters for self-adjoint elliptic Dirichlet forms with Lipschitz coefficients. In two dimensions we obtain best possible bounds for all p between $2 and infinity, up to logarithmic losses…

The purpose of this paper is threefold. First the natural extension of Riesz potentials to the context of quasi metric measure spaces for the class of upper doubling measures are studied on Lebesgue spaces, obtaining necessary and…

Under the standard assumptions on the variable exponent $p(x)$ (log- and decay conditions), we give a characterization of the variable exponent Bessel potential space $\mathfrak B^\alpha[L^{p(\cdot)}(\mathbb R^n)]$ in terms of the rate of…

In this paper, we consider the characterizations of the Lipschitz spaces and homogeneous Lipschitz spaces associated to the biharmonic operator $\Delta^2.$ With this characterizations, we prove the boundedness of the Bessel potentials,…

We derive sparse bounds for the bilinear spherical maximal function in any dimension $d\geq 1$. When $d\geq 2$, this immediately recovers the sharp $L^p\times L^q\to L^r$ bound of the operator and implies quantitative weighted norm…

We investigate the problem of establishing bilateral continuous embeddings of the uniformly localized Bessel potential spaces $H^{\gamma}_{r, \: unif}(\mathbb{R}^n)$ into the multiplier spaces between Bessel potential spaces with positive…

We study the boundedness of the Hilbert transform $H$ and the Hilbert maximal operator $H^*$ on weighted Lorentz spaces $\Lambda^p_u(w)$. We start by giving several necessary conditions that, in particular, lead us to the complete…

We study Riesz and Bessel potentials in the settings of Hankel transform, modified Hankel transform and Hankel-Dunkl transform. We prove sharp or qualitatively sharp pointwise estimates of the corresponding potential kernels. Then we…

In this paper we obtain the non - asymptotic estimations for Riesz's and Bessel's potential integral operators in the so - called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these inequalities.

This paper studies Hausdorff-Young-type inequalities within the framework of Lorentz spaces $L_{p,q}$. Focusing on the dependence of the associated constants on the integrability parameter $p$, we derive optimal bounds in the limiting case…

Let (X,\mu) be a measure space. For p, q\in (0,\infty] and arbitrary subsets P,Q of (0,\infty], we introduce and characterize some intersections of Lorentz spaces, denoted by ILp,Q(X,\mu), ILJ,q(X,\mu) and ILJ,Q(X,\mu).

We deal with the boundedness of the multilinear fractional integral operator $I_{\gamma,m}$ from a product of weighted Lebesgue spaces into adequate weighted Lipschitz spaces. Our results generalize some previous estimates not only for the…

$(L_p, L_q)$ estimates are obtained for oscillatory potentials $(K^\alphaf)(x)=\int\limits_{R^n}\frac{\exp(i|y|)}{|y|^{n-\alpha}}f(x-y)dy$, $0<\alpha<n$, $n\geq 2$, whose symbol has a singularity on the unit sphere. These potentials are…

The main result of this work is the proof of the boundedness of the Ornstein-Uhlenbeck semigroup $ \{T_t \}_{t\geq 0} $ in $ {\mathbb R}^d $ on Gaussian variable Lebesgue spaces under a condition of regularity on $p(\cdot)$ following…

We establish necessary and sufficient conditions on a weight pair $(v,w)$ governing the boundedness of the Riesz potential operator $I_{\alpha}$ defined on a homogeneous group $G$ from $L^p_{dec,r}(w, G)$ to $L^q(v, G)$, where…

In this paper, we develop a thorough analysis of the boundedness properties of the maximal operator for the Bochner-Riesz means related to the Fourier-Bessel expansions. For this operator, we study weighted and unweighted inequalities in…

In this article, we investigate the bilinear Riesz means $S^{\alpha }$ associated to the sublaplacian on the Heisenberg group. We prove that the operator $S^{\alpha }$ is bounded from $L^{p_{1}}\times L^{p_{2}}$ into $ L^{p}$ for $1\leq…

Given an $m$-tuple of weights $\vec{v}=(v_1,\dots,v_m)$, we characterize the classes of pairs $(w,\vec{v})$ involved with the boundedness properties of the multilinear fractional integral operator from…

We investigate the nonnegative solutions to the nonlinear integral inequality $u \ge I_{\alpha}\ast\big((I_\beta \ast u^p)u^q\big)$ a.e. in $\mathbb{R}^N$, where $\alpha, \beta\in (0,N)$, $p, q>0$ and $I_\alpha$, $I_\beta$ denote the Riesz…

We deal with the boundedness properties of higher order commutators related to some generalizations of the multilinear fractional integral operator of order $m$, $I_\alpha ^m$, from a product of weighted Lebesgue spaces into adequate…