相关论文: Mixed norm estimates for Hermite multipliers
Let $L=-\Delta +V$ with non-negative potential $V$ satisfying some appropriate reverse H\"older inequality. In this paper, we study the boundedness of the commutators of some singular integrals associated to $L$ such as Riesz transforms and…
We prove mixed inequalities for the Hardy-Littlewood maximal function $M^{\rho,\sigma}$, where $\rho$ is a critical radius function and $\sigma\geq 0$. We also exhibit and prove an extension of Cruz-Uribe, Martell and P\'erez extrapolation…
We deal with mixed weak estimates of Fefferman-Stein type for higher order commutators of Calder\'on-Zygmund operators with BMO symbol. The results obtained are Fefferman-Stein inequalities that include the estimates proved in…
Multiple Hermite polynomials are an extension of the classical Hermite polynomials for which orthogonality conditions are imposed with respect to $r>1$ normal (Gaussian) weights $w_j(x)=e^{-x^2+c_jx}$ with different means $c_j/2$, $1 \leq j…
In this paper, we consider a single-index mixed model with longitudinal data. A new set of estimating equations is proposed to estimate the single-index coefficient. The link function is estimated by using the local linear smoothing.…
We prove an analogue of Gutzmer's formula for Hermite expansions. As a consequence we obtain a new proof of a characterisation of the image of $ L^2(\R^n) $ under the Hermite semigroup. We also obtain some new orthogonality relations for…
A conjecture concerning some pairs of interfering estimates for some integrals is formulated in three equivalent versions. Its importance for the the Paley problem for plurisubharmonic functions and for certain classes of extremal problems…
In this paper we establish the boundedness of bilinear paraproducts on local BMO spaces. As applications, we also investigate the boundedness of bilinear Fourier integral operators and bilinear Coifman-Meyer multipliers on these spaces and…
We give integral representations for multiple Hermite and multiple Hermite polynomials of both type I and II. We also show how these are connected with double integral representations of certain kernels from random matrix theory.
In this paper, we find new integral representations for the generalized Hermite linear functional in the real line and the complex plane. As an application, new integral representations for the Euler Gamma function are given.
Regularity estimates for an integral operator with a symmetric continuous kernel on a convex bounded domain are derived. The covariance of a mean-square continuous random field on the domain is an example of such an operator. The estimates…
First we introduce the Bailleul-Hoshino's result [4], which links the theory of regularity structures and the paracontrolled calculus. As an application of their result, we give another algebraic proof of the multicomponent commutator…
We investigate H\"ormander spectral multiplier theorems as they hold on $X = L^p(\Omega),\: 1 < p < \infty,$ for many self-adjoint elliptic differential operators $A$ including the standard Laplacian on $\R^d.$ A strengthened matricial…
Shifted variants of (dyadic) Hardy-Littlewood maximal function and Stein's square function have played a significant role in the study of many important operators such as Calderon commutators, (bilinear) Hilbert transforms, multilinear…
We give Feffermain-Stein type inequalities related to mixed estimates for Calder\'on-Zygmund operators. More precisely, given $\delta>0$, $q>1$, $\varphi(z)=z(1+\log^+z)^\delta$, a nonnegative and locally integrable function $u$ and $v\in…
We call a kind of mappings induced by a kind of weighted Laplace operator as complex valued kernel $\alpha$-harmonic mappings. In this article, for this class of mappings, the Heinz type lemma is established, and the best Heinz type…
In this paper, starting with a relatively simple observation that the variational estimates of the commutators of the standard Calder\'on-Zygmund operators with the BMO functions can be deduced from the weighted variational estimates of the…
The main purpose of this paper is, in the general setting of the adjointable operators on Hilbert $C^*$-modules, to develop two new tools that can be applied to deal with the positive solutions of certain operator equations, the operator…
We prove various estimates for the asymptotics of counting functions associated to point sets of coherent frames and Riesz sequences. The obtained results recover the necessary density conditions for coherent frames and Riesz sequences for…
The notation of generalized Bessel multipliers is obtained by a bounded operator on $\ell^2$ which is inserted between the analysis and synthesis operators. We show that various properties of generalized multipliers are closely related to…