Generalized Knopp identities for homogeneous Hardy sums and Cochrane-Hardy sums

Mean Value of Hardy Sums over Short Intervals

The main purpose of this paper is to study the mean value properties of certain Hardy sums over short intervals by using the mean value theorems of the Dirichlet L-functions, and to give two interesting asymptotic formulae.

Binomial Sums and Identities

Green’s Formula and the Hardy-stein Identities

This is a collection of some known and some new facts on the holomorphic and the harmonic version of the Hardy-Stein identity as well as on their extensions to the real and the complex ball. For example, we prove that if f is holomorphic on the unit disk D, then ‖f‖Hp 3 |f(0)| + Z D |f(z)|p−2|f ′(z)|2(1− |z|) dA(z), (†) where H is the p-Hardy space, which improves a result of Yamashita [Proc. A...

Anisotropic Picone identities and anisotropic Hardy inequalities

In this paper, we derive an anisotropic Picone identity for the anisotropic Laplacian, which contains some known Picone identities. As applications, a Sturmian comparison principle to the anisotropic elliptic equation and an anisotropic Hardy type inequality are shown.

Character sums and MacWilliams identities

We show that certain character sums are intimately connected with MacWilliams identities for linear poset codes as well as usual linear codes. We also illustrate in some two poset codes that this method gives much shorter proofs than the ones using discrete Poisson summation formula. © 2004 Elsevier B.V. All rights reserved. MSC: primary 11L03; 94B60; secondary 94B05