Related papers: Reverse Holder inequalities revisited: Interpolati…
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…
Given a complete Riemannian manifold satisfying a weighted Poincar\'{e} inequality and having a bounded below Ricci curvature, various vanishing theorems for harmonic functions and harmonic 1-forms have been published. We generalized these…
In the dyadic case the union of the Reverse H\"{o}lder classes, $RH_p^d$ is strictly larger than the union of the Muckenhoupt classes $ A_p^d$. We introduce the $RH_1^d$ condition as a limiting case of the $RH_p^d$ inequalities as $p$ tends…
This paper is devoted to a new family of reverse Hardy-Littlewood-Sobolev inequalities which involve a power law kernel with positive exponent. We investigate the range of the admissible parameters and the properties of the optimal…
We investigate the convergence of entire Lagrange interpolations and of Hermite interpolations of exponential type in weighted $L^p$-spaces on the real line. The weights are reciprocals of entire functions and depend on the type and may be…
This paper discusses an abstract Kramer sampling theorem for functions within a reproducing kernel Hilbert space (RKHS) of vector valued holomorphic functions. Additionally, we extend the concept of quasi Lagrange-type interpolation for…
In this paper, we establish some new inequalities for class of SX(h,I) convex functions which are supermultiplicative or superadditive and nonnegative. And we also give some applications for special means.
We consider K-interpolation methods involving slowly varying functions. Let $\overline{A}_{\theta,*}^{\mathcal{L}}$ and $\overline{A}_{\theta,*}^{\mathcal{R}}$ $(0\leq\theta\leq1)$ be the so called ${\mathcal{L}}$ or ${\mathcal{R}}$…
In this paper we characterize the validity of the inequalities $\|g\|_{p,(a,b),\lambda} \le c \|u(x) \|g\|_{\infty,(x,b),\mu}\|_{q,(a,b),\nu}$ and $\label{eq.0.1.2} \|g\|_{p,(a,b),\lambda} \le c \|u(x)…
This paper is devoted to a new family of reverse Hardy-Littlewood-Sobolev inequalities which involve a power law kernel with positive exponent. We investigate the range of the admissible parameters and characterize the optimal functions. A…
We give some new refinements and reverses Young inequalities in both additive-type and multiplicative-type for two positive numbers/operators. We show our advantages by comparing with known results. A few applications are also given. Some…
Thom polynomials provide universal formulas for the fundamental class of singularity loci in terms of characteristic classes. Ohmoto extended this notion to SSM-Thom polynomials, which refine this description by capturing the richer…
We present dimension-free reverse H\"older inequalities for strong $A^*_p$ weights, $1\le p < \infty$. We also provide a proof for the full range of local integrability of $A_1^*$ weights. The common ingredient is a multidimensional version…
Let $n \geq 2$, let $\Omega \subset \mathbf{R}^n$ be a bounded domain with smooth boundary, and let $1 \leq p \leq 2$. We prove a reverse-Holder inequality for functions $u$ realizing the best constant in the Sobolev inequality, that is…
In a recent paper V. Vasyunin presented a proof of the reverse H\"older inequality with sharp constants for the weights satisfying the usual Muckenhoupt condition. In this paper we present the inverse, that is, we use the Bellman function…
We present reverse H\"older inequalities for Muckenhoupt weights in $\mathbb{R}^n$ with an asymptotically sharp behavior for flat weights, namely $A_\infty$ weights with Fujii-Wilson constant $(w)_{A_\infty}\to 1^+$. That is, the local…
In this paper, weighted norm inequalities with $A_p$ weights are established for the multilinear singular integral operators whose kernels satisfy $L^{r'}$-H\"ormander regularity condition. As applications, we recover a weighted estimate…
In this paper, we first introduce the new class of multiple weights $A^\vc_{\vec{p}}$ which is larger than the class of multiple weights in \cite{LOPTG}. Then, using this class of weights, we study the weighted norm inequalities for certain…
In a previous paper, we obtained several "compact versions" of Rubio de Francia's weighted extrapolation theorem, which allowed us to extrapolate the compactness of linear operators from just one space to the full range of weighted Lebesgue…
We consider the class of all non-negative on $\mathbb{R_+}$ functions such that each of them satisfies the Reverse H\"older Inequality uniformly over all intervals with some constant the minimum value of which can be regarded as the…