We study the boundedness properties of Rudin–Forelli-type operators associated to tubular domains over symmetric cones. As an application, we give a characterization of the topological dual space of the weighted Bergman space .

In this paper we consider the problem of existence of mild solutions to semilinear fractional heat equations with non-local initial conditions. We provide sufficient conditions for existence and regularity of such solutions.

In this paper, for R a commutative ring, with identity, of characteristic p, we look at the group G(R) of formal power series with coefficients in R, of the form

and the group operation being substitution. The results obtained give the exponent of the quotient groups Gn(R) of this group, n∈ℕ.

In an earlier “Note on Selection from a Normal Multivariate Population” the author considered the transformation of an n-variate normal population induced by “selection” operating to alter the parameters of frequency in a subset of p variates, while preserving normal frequency in the subset. The results were new in notation only; in substance they were first found by K. Pearson.

This paper computes the Box and Hausdorff dimensions of the intersections of the Sierpinski carpet with planar lines of rational slopes.

We consider the existence and multiplicity of standing-wave solutions

of nonlinear Schrödinger equations with electromagnetic fields and critical nonlinearity

Under suitable assumptions, we prove that it has at least one solution and that, for any m ∈ ℕ, it has at least m pairs of solutions.

In this paper, we study a time-independent fractional Schrödinger equation of the form (−Δ)su + V(x)u = g(u) in ℝN, where N ≥, s ∈ (0,1) and (−Δ)s is the fractional Laplacian. By variational methods, we prove the existence of ground state solutions when V is unbounded and the nonlinearity g is subcritical and satisfies the following geometry condition:

Let Ω be an open connected subset of the unit disc U, let E = U\Ω and let {Ωk} be a Whitney decomposition of U. If z(Q) is the centre of the “square” Q, if T is the unit circle and t = dist.(Q, T), we consider

where Ek = E ∩ Qk and c(Ek) is the capacity of Ek. We prove that the set E is minimally thin at τ ∈ T in U if and only if W(τ)< ∞. We study functions of type W and discuss the relation between certain results of Naim on minimal thinness [15], a minimum principle of Beurling [3], related results due to Dahlberg [7] and Sjögren [16] and recent work of Hayman-Lyons [15] (cf. also Bonsall [4]) and Volberg [19]. For simplicity, we discuss our problems in the unit disc U in the plane. However, the same techniques work for analogous problems in higher dimensions and in more complicated regions.

We prove new results on the existence, non-existence, localization and multiplicity of non-trivial radial solutions of a system of elliptic boundary value problems on exterior domains subject to non-local, nonlinear, functional boundary conditions. Our approach relies on fixed point index theory. As a by-product of our theory we provide an answer to an open question posed by do Ó, Lorca, Sánchez and Ubilla. We include some examples with explicit nonlinearities in order to illustrate our theory.

The aim of this paper is to present a sign-changing solution for a class of radially symmetric asymptotically linear Schrödinger equations. The proof is variational and the Ekeland variational principle is employed as well as a deformation lemma combined with Miranda’s theorem.

The homogeneous Riemannian structures on the three-dimensional Berger spheres, their corresponding reductive decompositions and the associated groups of isometries are obtained. The Berger 3-spheres are also considered as homogeneous almost contact metric manifolds.

Let E be a Banach sequence space with the property that if (αi) ∈ E and |βi|≦|αi| for all i then (βi) ∈ E and ‖(βi)‖E≦‖(αi)‖E. For example E could be co, lp or some Orlicz sequence space. If (Xn) is a sequence of real or complex Banach spaces, then E can be used to construct a vector sequence space which we will call the E sum of the Xn's and symbolize by ⊕EXn. Specifically, ⊕EXn = {(xn)|(xn)∈Xn and (‖xn‖)∈E}. The E sum is a Banach space with norm defined by: ‖(xn)‖ = ‖(‖xn‖)‖E. This type of space has long been the source of examples and counter-examples in the geometric theory of Banach spaces. For instance, Day [7] used E=lp and Xk=lqk, with appropriate choice of qk, to give an example of a reflexive Banach space not isomorphic to any uniformly conves Banach space. Recently VanDulst and Devalk [33] have considered Orlicz sums of Banach spaces in their studies of Kadec-Klee property.

We prove in this paper that if (T, G, ∂) is a perfect and aspherical (Ker ∂ = 1) crossed module, then it admits a universal central extension, whose kernel is the invariant H2(T, G, ∂), that we introduced in [9].

We present a wavelet characterization of anisotropic Besov spaces $B_{p,q}^{\bm{\alpha}}(\mathbb{R}^n)$, valid for the whole range $0\ltp,q\lt\infty$, and in terms of multi-resolution analyses with dilation adapted to the anisotropy of the space. Our proofs combine classical techniques based on Bernstein and Jackson-type inequalities, and nonlinear methods for the cases $p\lt1$. Among the consequences of our results, we characterize $B_{p,q}^{\bm{\alpha}}$ as a linear approximation space, and derive embeddings and interpolation formulae for $B_{p,q}^{\bm{\alpha}}$, which appear to be new in the literature when $p\lt1$.

AMS 2000 Mathematics subject classification: Primary 42B35; 42C40; 41A17

We prove that for a function f(z) transcendental and meromorphic in the plane and not of the form exp(az + b), we have either N(r, 1/ff″)≠0(T(r, f′/f)) or .

A note on this subject was read to the Edinburgh Mathematical Society in June 1951. Subsequently I had the benefit of conversations and correspondence with J. G. Brennan and I. R. Porteous, and substantial contributions from them are incorporated here, more than are acknowledged in detail below.

We answer a weaker version of the classification problem for the homotopy types of (n — 2)-connected closed orientable (2n — 1)-manifolds. Let n ≥ 6 be an even integer and let X be an (n — 2)-connected finite orientable Poincaré (2n — 1)-complex such that Hn-1 (X;ℚ) = 0 and Hn-1 (X;ℤ2) = 0. Then its loop space homotopy type is uniquely determined by the action of higher Bockstein operations on Hn-1 (X; ℤp) for each odd prime p. A stronger result is obtained when localized at odd primes.

Some properties of polynomials associated with strong distribution functions are given, including conditions for the polynomials to satisfy a three term recurrence relation. Strong distributions that are extensions to the four classical distributions are given as examples.

We are concerned with the following Kirchhoff-type equation

$$ - \varepsilon ^2M\left( {\varepsilon ^{2 - N}\int_{{\open R}^N} {\vert \nabla u \vert^2{\rm d}x} } \right)\Delta u + V(x)u = f(u),\quad x \in {{\open R}^N},\quad N{\rm \ges }2,$$

The purpose of this paper is to study the influence of $c$-supplemented minimal subgroups on the $p$-nilpotency of finite groups. We obtain ‘iff' and ‘localized' versions of theorems of Itô and Buckley on nilpotence, $p$-nilpotence and supersolvability.