相关论文: Mapping properties of fundamental harmonic analysi…

We prove sharp power-weighted strong type, weak type and restricted weak type inequalities for the heat and Poisson integral maximal operators, Riesz transform and a Littlewood-Paley type square function, emerging naturally in the harmonic…

In this paper we establish that the maximal operator and the Littlewood-Paley g-function associated with the heat semigroup defined by multidimensional Bessel operators are of weak type (1,1). Also, we prove that Riesz transforms in the…

We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood-Paley-Stein square functions, multipliers of Laplace transform type and…

We consider several harmonic analysis operators in the multi-dimensional context of the Dunkl Laplacian with the underlying group of reflections isomorphic to $\mathbb{Z}_2^n$ (also negative values of the multiplicity function are…

We prove variation and oscillation $L^p$-inequalities associated with fractional derivatives of certain semigroups of operators and with the family of truncations of Riesz transforms in the inverse Gaussian setting. We also study these…

This article focuses on $L^p$ estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square functions and Riesz transforms. We introduce four critical…

In this paper we establish the $L^p$-boundedness properties of the variation operators associated with the heat semigroup, Riesz transforms and commutator between Riesz transforms and multiplication by $BMO(R^n)$-functions in the…

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 extend the classical Bernstein inequality to a general setting including Schr{\"o}dinger operators and divergence form elliptic operators on Riemannian manifolds or domains. Moreover , we prove a new reverse inequality that can be seen…

In this paper we obtain quantitative weighted $L^p$-inequalities for some operators involving Bessel convolutions. We consider maximal operators, Littlewood-Paley functions and variational operators. We obtain $L^p(w)$-operator norms in…

We study Hardy space $H^1_L(X)$ related to a self-adjoint operator $L$ defined on Euclidean domain $X \subseteq \mathbb{R}^d$. Under certain assumptions on the heat semigroup $\exp(-tL)$ we prove characterization of $H^1_L(X)$ by the Riesz…

This is the third part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. For $L$ in some class of elliptic operators, we study weighted norm $L^p$ inequalities for singular…

In this paper we prove that the generalized (in the sense of Caffarelli and Calder\'on) maximal operators associated with heat semigroups for Bessel and Laguerre operators are weak type (1,1). Our results include other known ones and our…

Let $L$ be a second order divergence form elliptic operator with complex bounded measurable coefficients. The operators arising in connection with $L$, such as the heat semigroup and Riesz transform, are not, in general, of…

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 work we obtain sharp embedding inequalities for a family of conformally invariant integral extension operators. This family includes among others the classical Poisson extension operator and the extension operator with Riesz kernel.…

We characterize the Hardy space $H^1$ in the rational Dunkl setting associated with the reflection group $\mathbb Z_2^n$ by means of Riesz transforms. As a corollary we obtain a Riesz transform characterization of $H^1$ for product of…

We establish that the spectral multiplier $\frak{M}(G_{\alpha})$ associated to the differential operator $$ G_{\alpha}=- \Delta_x +\sum_{j=1}^m{{\alpha_j^2-1/4}\over{x_j^2}}-|x|^2 \Delta_y \; \text{on} (0,\infty)^m \times \R^n,$$ which we…

Let $\lambda>0$, $p\in((2\lz+1)/(2\lz+2), 1]$, and $\triangle_\lambda\equiv-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ be the Bessel operator. In this paper, the authors establish the characterizations of atomic Hardy spaces $H^p((0,…

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,…