Related papers: Sharp Weighted $L^2$ inequalities for square funct…

This paper aims to characterize the function appearing in the weighted Hermite-Hadamard inequality. We provide improved inequalities for the weighted means as applications of the obtained results. Modifications of the weighted…

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…

We prove weak type inequalities for a large class of noncommutative square functions. In conjunction with BMO type estimates, interpolation and duality, we will obtain the corresponding equivalences in the whole Lp scale. The main novelty…

Criteria for the fulfillment of inequalities in weighted smoothness function spaces of Besov type with Riemann-Liouville operators of natural orders on the real axis and semi-axes are found. The obtained estimates are refined under…

We find sharp constants in the symmetric integral form of the John-Nirenberg inequality. The result is based upon computation of a new interesting Bellman function.

For certain non compact Riemannian manifolds with ends, we obtain Littlewood-Paley type estimates on (weighted) Lp spaces, using the usual square function defined by a dyadic partition.

We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…

We consider intrinsic square functions defined using (log-)Dini continuous test functions on spaces of homogeneous type. We prove weighted estimates with optimal (at least in the Euclidean case) dependence on the aperture of the cone used…

We prove sharp homogeneous improvements to $L^1$ weighted Hardy inequalities involving distance from the boundary. In the case of a smooth domain, we obtain lower and upper estimates for the best constant of the remainder term. These…

Let $\mathcal{L}_a$ be a Schr\"odinger operator with inverse square potential $a|x|^{-2}$ on $\mathbb{R}^d, d\geq 3$. The main aim of this paper is to prove weighted estimates for fractional powers of $\mathcal{L}_a$. The proof is based on…

We give a H\"ormander type $L^2-$estimate for the $\bar{\partial}-$equation with respect to the measure $\delta_\Omega^{-\alpha}dV$, $\alpha<1$, on any bounded pseudoconvex domain with $C^2-$boundary. Several applications to the function…

We unify several Bellman function problems into one setting. For that purpose we define a class of functions that have, in a sense, small mean oscillation (this class depends on two convex sets in $\mathbb{R}^2$). We show how the unit ball…

We study the problem of multivariate $L_2$-approximation of functions in a weighted Korobov space using a median lattice-based algorithm recently proposed by the authors. In the original work, the algorithm requires knowledge of the…

We find necessary and sufficient conditions for the validity of weighted Rellich and Calderon-Zygmund inequalities in L^p, 1 \leq p \leq \infty, in the whole space and in the half-space with Dirichlet boundary conditions. General operators…

We study the boundedness of commutators of the Hardy-Littlewood maximal function and the sharp maximal function on weighted Morrey spaces when the symbols of the commutators belong to weighted Lipschitz spaces. Some new characterizations…

We find the general form of supersymmetric invariant two point functions. By imposing supersymmetric positivity we obtain the general supersymmetric K\"allen-Lehmann representation.

A Hardy-Littlewood integral inequality on finite intervals with a concave weight is established. Given a function f on an interval [a,b], it is shown that the square of the weighted L^2 norm of its derivative f' is bounded by the product of…

The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalites for functions. This will allow us to prove a local subelliptic Sobolev inequality with the optimal…

In this paper, we will obtain the strong type and weak type estimates for vector-valued analogues of intrinsic square functions in the generalized weighted Morrey spaces $M^{\Phi,\varphi}_{w}(\mathbb{R}^n)$. We study the boundedness of…

We consider the weighted least squares spline approximation of a noisy dataset. By interpreting the weights as a probability distribution, we maximize the associated entropy subject to the constraint that the mean squared error is…