Related papers: Characterizations for arbitrary B\'ekoll\'e-Bonami…
The inequality of Berwald is a reverse-H\"older like inequality for the $p$th average, $p\in (-1,\infty),$ of a non-negative, concave function over a convex body in $\mathbb{R}^n.$ We prove Berwald's inequality for averages of functions…
Some inequalities and reverses of classic H\"{o}lder and Minkowski types are obtained for scalar Birkhoff weak integrable functions with respect to a non-additive measure.
Let $n\geqslant 3$ be an integer. For the Bekoll\'e-Bonami weight $\omega$ on the real unit ball $\mathbb{B}_n$, we obtain the following sharp one-weight estimate for the $\mathcal{H}$-harmonic Bergman projection: for $1<p<\infty$ and…
In this paper we establish sharp weighted bounds (Buckley type theorems) for one{sided maximal and fractional integral operators in terms of one{sided $A_p$ characteristics. Appropriate sharp bounds for strong maximal functions, multiple…
In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen's type and Jensen-Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen's…
In the Euclidean setting, the Fujii-Wilson-type $A_\infty$ weights satisfy a Reverse H\"older Inequality (RHI) but in spaces of homogeneous type the best known result has been that $A_\infty$ weights satisfy only a weak Reverse H\"older…
Subject to a range of side conditions, the two weight inequality for the Hilbert transform is characterized in terms of (1) a Poisson A_2 condition on the weights (2) A forward testing condition, in which the two weight inequality is tested…
The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The statistics of complementary…
We prove a self-improving property for reverse H{\"o}lder inequalities with non-local right hand side. We attempt to cover all the most important situations that one encounters when studying elliptic and parabolic partial differential…
The Hodge equations for 1-forms are studied on Beltrami's projective disc model for hyperbolic space. Ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments. An existence theorem for…
A plethora of spaces in Functional Analysis (Braun-Meise-Taylor and Carleman ultradifferentiable and ultraholomorphic classes; Orlicz, Besov, Lipschitz, Lebesque spaces, to cite the main ones) are defined by means of a weighted structure,…
The aim of this paper is to study two-weight norm inequalities for fractional maximal functions and fractional Bergman operator defined on the upper-half space. Namely, we characterize those pairs of weights for which these maximal…
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…
A strong version of the Orlicz maximal operator is introduced and a natural $B_p$ condition for the rectangle case is defined to characterize its boundedness. This fact let us to describe a sufficient condition for the two weight…
A reverse H\"older inequality is established on the space of K\"ahler metrics in the first Chern class of a Fano manifold X endowed with Darvas L^{p}-Finsler metrics. The inequality holds under a uniform bound on a twisted Ricci potential…
We prove the weighted $L^p$ regularity of the ordinary Bergman projection on certain pseudoconvex domains where the weight belongs to an appropriate generalization of the B\'{e}koll\`{e}-Bonami class. The main tools used are estimates on…
We obtain inequalities of H\"{o}lder and Minkowski type with weights generalizing both the case of weights with alternating signs and the classical case of non-negative weights.
We provide a precise statement and self contained proof of a Sobolev inequality (cf. [A, page 236 and page 237]) stated in the original paper. Higher order and fractional inequalities are treated as well.
We propose algebraic criteria that yield sharp H\"{o}lder types of inequalities for the product of functions of Gaussian random vectors with arbitrary covariance structure. While our lower inequality appears to be new, we prove that the…
In this paper, we introduce the notion of conditional $h$-convex functions and we prove an operator version of the Jensen inequality for conditional $h$-convex functions. Using this type of functions, we give some refinements for Ky-Fan's…