Related papers: A Decomposition for Hardy Martingales III

We develop a theory of Jacobi polynomials for parabolic subgroups of finite reflection groups that specializes to the cases studied by Heckman and Opdam in which the whole group and the trivial group are considered. For the intermediate…

We prove Hardy inequalities for the conformally invariant fractional powers of the sublaplacian on the Heisenberg group $\mathbb{H}^n$. We prove two versions of such inequalities depending on whether the weights involved are non-homogeneous…

We prove derived McKay correspondence in special cases and the decomposition of toric K-equivalence into flops.

We provide an analogue of Gundy's decomposition for L1-bounded non-commutative martingales. An important difference from the classical case is that for any L1-bounded non-commutative martingale, the decomposition consists of four…

We use Matrix Analysis to prove a general decoupling inequality for finite Gaussian vectors, in identifying a new region of the inherent $p$ exponent, for the validity of this one.

We prove several Sobolev inequalities, which are then used to establish a fractional Hardy-Sobolev- Maz'ya inequality on the upper halfspace.

In this paper some important inequalities are revisited. First, as motivation, we give another proof of the Hardy's inequality applying convenient vector fields as introduced by Mitidieri, see [6]. Then, we investigate a particular case of…

New Hardy and Sobolev type inequalities involving $L^1$-norms of scalar and vector-valued functions in $\Bbb{R}^n$ are obtained. The work is related to some problems stated in the recent paper by Bourgain and Brezis

For any lattice polytope $P$, we consider an associated polynomial $\bar{\delta}_{P}(t)$ and describe its decomposition into a sum of two polynomials satisfying certain symmetry conditions. As a consequence, we improve upon known…

We find solutions for a linear deformation of the symmetric three-term recursion relation. The orthogonal polynomials of the first and second kind associated with the deformed relation are obtained. The new density (weight) function is…

We provide a version of the Stein-Weiss inequality for arbitrary martingales.

Assuming that a function and its Fourier transform are dominated by a Gaussian, Vemuri found a sharp estimate for the decay rate of the Hermite coefficients in terms of the variance of the dominating Gaussian. Here we show that under the…

We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of…

In this paper, we prove some new inequalities of Hadamard-type for s-convex functions on the co-ordinates.

We develop the theory of variable exponent Hardy spaces. Analogous to the classical theory, we give equivalent definitions in terms of maximal operators. We also show that distributions in these spaces have an atomic decomposition including…

The V-systems are special finite sets of covectors which appeared in the theory of the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. Several families of V-systems are known but their classification is an open problem. We…

In this paper, we focus on three main objectives related to Hardy-type inequalities on Cartan-Hadamard manifolds. Firstly, we explore critical Hardy-type inequalities that contain logarithmic terms, highlighting their significance.…

We obtain Calder{\'o}n-Zygmund estimates for some degenerate equations of Kolmogorov type with inhomogeneous coefficients. We then derive the well-posedness of the martingale problem associated to related degenerate operators, and therefore…

We classify the three-dimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vector-valued modular forms. We then demonstrate how such representations may be…

An important concept of convexificators has been extended to Hadamard manifolds in this paper. The mean value theorem for convexificators on the Hadamard manifold has also been derived. Monotonicity of the bounded convexificators has been…