相关论文: The structure of weight and function classes with …

Using a wide array of machinery from diverse fields across mathematics, we provide a construction of a measure on the real line which is doubling on all $n$-adic intervals for any finite list of $n\in\mathbb{N}$, yet not doubling overall.…

We unite two themes in dyadic analysis and number theory by studying an analogue of the failure of the Hasse principle in harmonic analysis. Explicitly, we construct an explicit family of measures on the real line that are $p$-adic and…

In this paper, we prove a structure theorem for the infinite union of $n$-adic doubling measures via techniques which involve far numbers. Our approach extends the results of Wu in 1998, and as a by product, we also prove a classification…

A series of longstanding questions in harmonic analysis ask if the intersection of all prime ``$p$-adic versions" of an object, such as a doubling measure, or a Muckenhoupt or reverse H\"older weight, recovers the full object. Investigation…

Muckenhoupt and Reverse H\"{o}lder classes of weights play an important role in harmonic analysis, PDE's and quasiconformal mappings. In 1974 Coifman and Fefferman showed that a weight belongs to a Muckenhoupt class $A_p$ for some…

Working on doubling metric spaces, we construct generalised dyadic cubes adapting ultrametric structure. If the space is complete, then the existence of such cubes and the mass distribution principle lead into a simple proof for the…

Linear codes with a few weights are an important class of codes in coding theory and have attracted a lot of attention. In this paper, we present several constructions of $q$-ary linear codes with two or three weights from vectorial…

Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of $p$-ary linear codes with two or three weights are constructed…

The purpose of this paper is to study the special values of the standard $L$-functions for quaternionic modular forms using the doubling method. We obtain an integral representation for the $L$-function twisted by a character and construct…

In this paper, we employ general results on the value distributions of perfect nonlinear functions from $\mathbb{F}_{p^m}$ to $\mathbb{F}_p$ together with a specific group action to give a unified approach to determining the weight…

By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy $p$-harmonic and $p$-quasiharmonic functions, we classify proper metric spaces equipped with a locally doubling measure supporting a local…

Linear codes with a few weights can be applied to secrete sharing, authentication codes, association schemes and strongly regular graphs. For an odd prime power $q$, we construct a class of three-weight $\F_q$-linear codes from quadratic…

Let $X$ be a metric space equipped with a doubling measure. We consider weights $w(x)=\operatorname{dist}(x,E)^{-\alpha}$, where $E$ is a closed set in $X$ and $\alpha\in\mathbb R$. We establish sharp conditions, based on the Assouad…

This paper is concerned with two generalizations of the Hopf algebra of symmetric functions that have more or less recently appeared. The Hopf algebra of noncommutative symmetric functions and its dual, the Hopf algebra of quasisymmetric…

Successive divisions of compact metric spaces appear in many different areas of mathematics such as the construction of self-similar sets, Markov partitions associated with hyperbolic dynamical systems, dyadic cubes associated with a…

In this paper we consider the question of whether the doubling character of a measure supported on a subset of $\RR^m$ determines the regularity of its support (in a classical sense). This problem was studied by David, Kenig and Toro for…

The objective of this paper is to construct a class of linear codes with two nonzero weights and three nonzero weights by using the general trace functions, which weight distributions has been determined. These linear codes contain some…

On metric spaces equipped with doubling measures, we prove that a differentiability theorem holds for Lipschitz functions if and only if the space supports nontrivial (metric) derivations in the sense of Weaver that satisfy an additional…

By adapting the moment method developed by Granville and Soundararajan [17], Khan, Milinovich and Subedi [24] recently obtained a weighted version of the Erd\H{o}s--Kac theorem for $\omega(n)$ with multiplicative weight $d_k(n)$, where…

Donnay, Garcia and Rouse classified nonsingular quadratic forms $Q$ with integral coefficients and prime numbers $p$ such that the set of quotients of values of $Q$ attained for integer arguments is dense in the field of $p$-adic numbers.…