L-Poisson integral representations of solutions of the Hua system on the bounded symmetric domain SU(n,n)/S(U(n)×U(n))

Let positive definite} be the matrix ball of rank n and let H_D be the associated Hua operator. For a complex number λ, such that Reiλ>n−1 we give a necessary and sufficient condition on solutions F of the following Hua system of differential equations on D:

     

Eigenvalues of p(x)-Laplacian Dirichlet problem

This paper studies the eigenvalues of the p(x)-Laplacian Dirichlet problem

     

L stability estimate for a one-dimensional Boltzmann equation with inelastic collisions

In this paper, we study the L¹ stability of a one-dimensional Boltzmann equation on the line with inelastic collisions in Rend. Sem. Mat. Fis. Milano 67 (1997) 169-179. Under the suitable assumptions on the initial data, we construct a nonlinear functional which measures L¹ distance between two mild solutions, and is nonincreasing in time t. Using the time-decay estimate of , we show that mild solutions are L¹-stable:

     

A Knobloch-type result for p(t)-Laplacian systems

We consider the periodic boundary value problem of ordinary differential systems with p(t)-Laplacian of the form

     

Dynamics of the w function and primes

We begin by defining a function w on the set

     

On spaces which are D, linearly D and transitively D

In this note, we comment on D-spaces, linearly D-spaces and transitively D-spaces. We show that every meta-Lindelöf space is transitively D. If X is a weak -refinable TD-scattered space, then X is transitively D, where TD is the class of all transitively D-spaces. If X is a weak -refinable -scattered space, then X is a D-space, where is the class of all D-spaces, and hence every weak -refinable (or submetacompact) scattered space is a D-space. This gives a positive answer to a question mentioned by Martínez and Soukup. In the last part of this note, we show that if X is a weak -refinable space then X is linearly D.     

On the equipartition of energy for the critical NLW

We study some qualitative properties of global solutions to the following focusing and defocusing critical NLW:

     

On p-adic q-l-functions and sums of powers

In this paper, we give an explicit p-adic expansion of

     

On the parity of exponents in the standard factorization of n!

Let p₁,p₂,… be the sequence of all primes in ascending order. The following result is proved: for any given positive integer k and any given , there exist infinitely many positive integers n with

     

When subset-sums do not cover all the residues modulo p

Let . We prove that a subset of , where p is a prime number, with cardinality larger than such that its subset sums do not cover has an automorphic image which is rather concentrated; more precisely, there exists s prime to p such that

     

A note on BMO and its application

In this note, at first we will point out a fact which is implicitly contained in the original paper of John and Nirenberg [Comm. Pure Appl. Math. 14 (1961) 415-426]. If a BMO(Rn) function f satisfies (obviously if the value of left term is finite it must be zero), then there holds

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Generalized composition operators from F(p, q, s) spaces to Bloch-type spaces

Let H(B) denote the space of all holomorphic functions on the unit ball B of Cⁿ. Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0. In this paper, we investigate the boundedness and compactness of the generalized composition operator

     

A landau-type construction concerning (L)′ ⊂ L

Let 1 ? p < ∞ and 1/p + 1/q = 1. For a locally finite measure space (X, S, μ) and a measurable complex-valued function f ∉ L^q functions g ∈ L^p may be constructed explicitly which satisfy

     

Some Zygmund type L inequalities for polynomials

Let p(z) be a polynomial of degree n which does not vanish in |z|<k. It is known that for each q>0 and k?1,

     

Existence of multiple positive solutions for one-dimensional p-Laplacian

In this paper we consider the multipoint boundary value problem for one-dimensional p-Laplacian

     

Derivatives of the L-cosine transform

The L^p-cosine transform of an even, continuous function is defined by