This presentation is in two parts. First, we recall the deenition of two types of asymptotic expansions known as nested form and nested expansions. This theory makes it possible to adapt the asymptotic scale to the function under expansion and is based on the theory of Hardy elds 1]. Next, we suggest a reformulation of nested forms in terms of generalized products called star products, and a pr...

In this article we give a unifying approach to the theory of fundamental sequences and their related Hardy hierarchies of number-theoretic functions and we show the equivalence of the new approach with the classical one. Mathematics Subject Classification: 03D20, 03F15, 03E10.

The boundedness for the multilinear Marcinkiewicz operators on certain Hardy and Herz-Hardy spaces are obtained.

We propose and prove a trinomial version of the celebrated Bailey’s lemma. As an application we obtain new fermionic representations for characters of some unitary as well as nonunitary models of N = 2 superconformal field theory (SCFT). We also establish interesting relations between N = 1 and N = 2 models of SCFT with central charges 3 2 ( 1− 2(2−4ν) 2(4ν) ) and 3 ( 1− 2 4ν ) . A number of ne...

The operator-valued Schur-class is defined to be the set of holomorphic functions S mapping the unit disk into the space of contraction operators between two Hilbert spaces. There are a number of alternate characterizations: the operator of multiplication by S defines a contraction operator between two Hardy Hilbert spaces, S satisfies a von Neumann inequality, a certain operator-valued kernel ...

Here and throughout this paper 191 is strictly less than one. Two new proofs of these identities have recently been announced. The first, by Lepowsky and Wilson [7], uses a Lie algebraic interpretation of the identities. The second, by Garsia and Milne (41, relies on the combinatorial interpretation and establishes the correspondence between the partitions which are counted by each side. Both o...

In this paper, we study some systems of integral equations, including those related to Hardy-Littlewood-Sobolev (HLS) inequalities. We prove that, under some integrability conditions, the positive regular solutions to the systems are radially symmetric and monotone about some point. In particular, we established the radial symmetry of the solutions to the Euler-Lagrange equations associated wit...