We give a direct proof that wis an A∞+(g) weight if and only if w satisfies a one-sided, weighted reverse Hölder inequality.

In dealing with the spectral synthesis property for a plane curve with nonzero curvature, a key step is to have a uniform L∞ estimate for some smoothing operators related to the curve. In this paper, we will show that the same L∞ estimate holds true for a plane curve that may have zero curvature.

We consider the rings of invariants RG, where R is the symmetric algebra of a tensor product between two vector spaces over the field Fp andG = Un × Um. A polynomial algebra is constructed and these invariants provide Chern classes for the modular cohomology of Un+m.

A general lacunary Littlewood-Paley type theorem is proved, which applies in a variety of settings including Jacobi polynomials in [0, 1], SU(2), and the usual classical trigonometric series in [0, 2π). The theoremis used to derive new results for Lp multipliers on SU(2) and Jacobi Lp multipliers.

Let A be a finite abelian group and M be a branched cover of an homology 3-sphere, branched over a link L, with covering group A. We show that H1(M; Z[1/|A|]) is determined as a Z[1/|A|][A]-module by the Alexander ideals of L and certain ideal class invariants.

Suppose A is a unital C*-algebra and m:A → B(X) is unital bounded algebra homomorphism where B(X) is the algebra of all operators on a Banach space X. When X is a Hilbert space, a problem of Kadison [9] asks whether m is similar to a *-homomorphism. Haagerup [5] has shown that the answer is positive when m(A) has a cyclic vector or whenever m is completely bounded. We use this to show m(A) is reflexive (Alg Lat m(A) = m(A)−sot) whenever X is a Hilbert space. Our main result is that whenever A is a separable GCR C*-algebra and X is a reflexive Banach space, then m(A) is reflexive.

If f0: Ω ⊂ ℝm → Sn is a weakly p-harmonic map from a bounded smooth domain Ω in ℝm (with 2 < p < m) into a sphere and if f0 is not stationary p-harmonic, then there exist infinitely many weak solutions of the p-harmonic flow with initial and boundary data f0, i.e., there are infinitely many global weak solutions f :Ω × ℝ → ⊂ Sn of

We also show that there exist non-stationary weakly (m − 1)-harmonic maps f0: Bm → Sm−1.

We give an elementary potential-theoretic proof of a theorem of G. Johnsson: all solutions of Cauchy’s problems for the Laplace equations with an entire data on a sphere extend harmonically to the whole space RN except, perhaps, for the center of the sphere.

A new shorter proof of the existence of index pairs for discrete dynamical systems is given. Moreover, the index pairs defined in that proof are stable with respect to small perturbations of the generating map. The existence of stable index pairs was previously known in the case of diffeomorphisms and flows generated by smooth vector fields but it was an open question in the general discrete case.

A characterisation of the range of a homomorphism between two commutative group algebras is presented which implies, among other things, that this range is closed. The work relies mainly on the characterisation of such homomorphisms achieved by P. J. Cohen.

Criteria for local uniform rotundity and midpoint local uniform rotundity in Orlicz-Lorentz spaces with the Luxemburg norm are given. Strict K-monotonicity and Kadec-Klee property are also discussed.

Let B be a Brownian motion on R, B(0) = 0, and let f (t, x) be continuous. T. Salisbury conjectured that if the total variation of f (t, B(t)), 0 ≤ t ≤ 1, is finite P-a.s., then f does not depend on x. Here we prove that this is true if the expected total variation is finite.

We show that if A is a torsion-free word hyperbolic group which belongs to class (Q), that is all finitely generated subgroups of A are quasiconvex in A, then any maximal cyclic subgroup U of A is a Burns subgroup of A. This, in particular, implies that if B is a Howson group (that is the intersection of any two finitely generated subgroups is finitely generated) then A *UB, ⧼A, t | Ut = V⧽ are also Howson groups. Finitely generated free groups, fundamental groups of closed hyperbolic surfaces and some interesting 3-manifold groups are known to belong to class (Q) and our theorem applies to them. We also describe a large class of word hyperbolic groups which are not Howson.

We generalize Siegel modular forms and construct an exact sequence for the cohomology of locally symmetric varieties which plays the role of the Eichler-Shimura isomorphism for such generalized Siegel modular forms.

We consider the problem: If K is a compact normal operator on a Hilbert module E, and f ∈ C0(SpK) is a function which is zero in a neighbourhood of the origin, is f(K) of finite rank? We show that this is the case if the underlying C*-algebra is abelian, and that the range of f(K) is contained in a finitely generated projective submodule of E.

Let 𝔾p,q(𝔽) be the Grassmann space of all q-dimensional 𝔽-vector subspaces of 𝔽p, where 𝔽 stands for ℝ, ℂ or ℍ (the quaternions). Here 𝔾p,q(𝔽) is regarded as a real algebraic variety. The paper investigates which C∞ maps from a nonsingular real algebraic variety X into 𝔾p,q(𝔽) can be approximated, in the C∞ compact-open topology, by real algebraic morphisms.

The main purpose of this paper is to study groups G1, G2 such that H*(BG1, Z/p) is isomorphic to H*(BG2, Z/p) in U, the category of unstable modules over the Steenrod algebra A, but not isomorphic as graded algebras over Z/p.

An example is constructed to show that the J0-radical of a matrix nearring can be an intermediate ideal. This solves a conjecture put forward in [1].

On caractérise les corps K satisfaisant le théorème de l’axe principal à l’aide de propriétés des formes trace des extensions finies de K. Grâce à la caract érisation de ces mêmes corps due à Waterhouse, on retrouve à partir de là, de façon élémentaire, un résultat de Becker selon lequel un pro-2-groupe qui se réalise comme groupe de Galois absolu d’un tel corps K est engendré par des involutions.

We study the existence of solutions of the semilinear equations (1) in which the non-linearity g may grow superlinearly in u in one of directions u → ∞ and u → −∞, and (2) −Δu + g(x, u) = h, in which the nonlinear term g may grow superlinearly in u as |u| → ∞. The purpose of this paper is to obtain solvability theorems for (1) and (2) when the Landesman-Lazer condition does not hold. More precisely, we require that h may satisfy are arbitrarily nonnegative constants, . The proofs are based upon degree theoretic arguments.