Related papers: Extrapolation on Hardy spaces and applications

We generalize Rado's extension theorem to complex spaces.

We derive from Jefimenko's equations a multipole expansion in order to obtain the exact expressions for the electric and magnetic fields of an electric dipole with an arbitrary time dependence. A few comments are also made about the usual…

We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection with linear differential equations. Next we prove normalization…

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…

Multilinear trace restriction inequalities are obtained for Hardy's inequality. More generally, detailed development is given for new multilinear forms for Young's convolution inequality, and a new proof for the multilinear…

We investigate Hardy spaces $H^1_L(X)$ corresponding to self-adjoint operators $L$. Our main aim is to obtain a description of $H^1_L(X)$ in terms of atomic decompositions similar to such characterisation of the classical Hardy spaces…

This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct…

We study tensor categories that interpolate the representation categories of finite classical groups. There are (at least) two ways to approach these categories: via ultraproducts and via oligomorphic groups. Both have strengths and…

The notion of prolongation of an algebraic variety is developed in an abstract setting that generalises the difference and (Hasse) differential contexts. An interpolating map that compares the prolongation spaces with algebraic jet spaces…

Let $M$ be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces $H^p$ of differential forms on $M$ and give various characterizations of them, including an atomic decomposition.…

We introduce and discuss a multivariate version of the classical median that is based on an equipartition property with respect to quarter spaces. These arise as pairwise intersections of the half-spaces associated with the coordinate…

The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several…

This contribution is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg and weighted logarithmic Hardy inequalities. These results have been obtained in…

We propose a method for designing accurate interpolation formulas on the real axis for the purpose of function approximation in weighted Hardy spaces. In particular, we consider the Hardy space of functions that are analytic in a strip…

In this paper we survey many results on the Dirichlet space of analytic functions. Our focus is more on the classical Dirichlet space on the disc and not the potential generalizations to other domains or several variables. Additionally, we…

Some finite series of harmonic numbers involving certain reciprocals are evaluated. Products of such reciprocals are expanded in a sum of the individual reciprocals, leading to a computer program. A list of examples is provided.

An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical field examples. The formulation presented and the…

Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces and homotopy invariant fixed point theory. We show that in many cases,…

Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ for all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact on $L^{p_1}(w_1)$ for some $w_1\in A_{p_1}(\mathbb R^d)$. Then $T$ is…

We extend the theory of Rubio de Francia extrapolation, including off-diagonal, limited range, and $A_{\infty}$ extrapolation, to the weighted variable Lebesgue spaces. As a consequence we are able to show that a number of different…