Related papers: A thin-thick Decomposition for Hardy Martingales

In this paper, a new class of convex functions as a generalization of convexity which is called (h-m)-convex functions and some properties of this class is given. We also prove some Hadamard's type inequalities.

In this review paper, we survey Hardy type inequalities from the point of view of Folland and Stein's homogeneous groups. Particular attention is paid to Hardy type inequalities on stratified groups which give a special class of homogeneous…

We present simple proofs of a discrete fractional and non-fractional Hardy inequality, Our constants are explicit, but not optimal. In the class of power weights, we get a complete picture of when the non-fractional Hardy inequality holds,…

We obtain a new square function characterization of the weak Hardy space $H^{p,\infty}$ for all $p\in(0,\iy)$. This space consists of all tempered distributions whose smooth maximal function lies in weak $L^p$. Our proof is based on…

This work is about a new class of martingales: the vertical martingales. We construct the vertical martingale for smooth submersions and we develop a stochastic calculus for one. Furthermore, we gives a stochastic characterization for…

In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.

In this article, we establish weighted strong and weak type inequalities for non-commutative square functions that naturally arise in the analysis of differences between ball averages and martingale sequences within the framework of group…

In this work, we give a decomposition of a martingale into three martingales with applications to certain types of inequalities in the new theory of Stochastic Analysis in Vector Lattices

Associated to the class of restricted-weak type weights for the Hardy operator, we find a new class of Lorentz spaces for which the normability property holds. This result is analogous to the characterization given by Sawyer for the…

We give an exact formula for the Bellman function of the weak type of martingale transform. We also give the extremal functions (actually extremal sequences of functions). We find them using the precise form of the Bellman function. The…

In this paper K closedness is proved in the case of the couple of real Hardy spaces in the corresponding couple of Lebesgue spaces. This means roughly that any measurable decomposition of an analytic function gives rise to an "analytic"…

We strengthen H\"older's inequality. The new family of sharp inequalities we obtain might be thought of as an analog of Pythagorean theorem for the $L^p$ spaces. Our reasonings rely upon Bellman functions of four variables.

In this article, we present weighted norm inequality for a fractional one-sided minimal function. We prove weighted weak and strong type norm inequalities for the one-sided minimal function on $\mathbb{R}.$ We construct two weight classes…

This is the first part of our work on Zariski decomposition structures, where we study Zariski decompositions using Legendre-Fenchel type transforms. In this way we define a Zariski decomposition for curve classes. This decomposition…

We give a weak factorization proof of the Hardy space $H^{p}(\mathbb{R}^{n})$ in the multilinear setting, for $\frac{n}{n+1} < p <1$. As a consequence, we obtain a characterization of the boundedness of the commutator $[b,T]$ from…

We establish various Hardy inequalities involving the distance function from submanifolds of Riemannian manifolds, where the natural weights are expressed in terms of bounds of the mean curvature of the submanifold and sectional/Ricci…

A new proof is given of the atomic decomposition of Hardy spaces Hp, in the classical setting of Rn. The new method can be used to establish atomic decomposition of maximal Hardy spaces in general setting and non classical settings.

In this paper, we present a short proof of Halin's grid theorem.

By analyzing an optimization problem over orthogonal matrices, we prove a generalization of the Hardy-Littlewood-P\'olya rearrangement inequality to positive definite matrices. The inequality is then extended to rectangular matrices. Using…

In this work, we prove that weak compactness of composition operator on $H^{1}(U^{n})$ coincides with its compactness. We also characterize bounded and compact composition operators on $H^{1}(U^{n}).$\