In the study of hereditary Noetherian rings, it is clear that hereditary Noetherian prime rings will play a central role (see, for example, [12]). Here we study the (two-sided) ideals of an hereditary Xoetherian prime ring and, as a consequence, ascertain the structure of factor rings and torsion modules. The torsion theory represents a generalization of similar results about Dedekind prime rin...

We obtain a weak type (1, 1) estimate for a maximal operator associated with the classical rough homogeneous singular integrals TΩ. In particular, this provides a different approach to a sparse domination for TΩ obtained recently by Conde-Alonso, Culiuc, Di Plinio and Ou [5].

For a Banach space X, let B(X) denote the Banach algebra of all continuous linear operators on X. First, we study the lattice of closed ideals in B(Jp), where 1 < p < ∞ and Jp is the pth James space. Our main result is that the ideal of weakly compact operators is the unique maximal ideal in B(Jp). Applications of this result include the following. (i) The Brown–McCoy radical of B(X), which by ...

We develop some new topological tools to study maximal subgroups of free idempotent generated semigroups. As an application, we show that the rank 1 component of the free idempotent generated semigroup of the biordered set of a full matrix monoid of size n×n,n > 2 over a division ring Q has maximal subgroup isomorphic to the multiplicative subgroup of Q.

We prove in this paper some sharp weighted inequalities for the vector–valued maximal function Mq of Fefferman and Stein defined by Mqf(x) = ( ∞ ∑ i=1 (Mfi(x)) q )1/q , where M is the Hardy–Littlewood maximal function. As a consequence we derive the main result establishing that in the range 1 < q < p < ∞ there exists a constant C such that ∫ Rn Mqf(x) p w(x)dx ≤ C ∫ Rn |f(x)|qM [ p q ]+1 w(x)d...

We are concerned with surjectivity of perturbations of maximal monotone operators in non-reflexive Banach spaces. While in a reflexive setting, a classical surjectivity result due to Rockafellar gives a necessary and sufficient condition to maximal monotonicity, in a nonreflexive space we characterize maximality using a “enlarged” version of the duality mapping, introduced previously by Gossez....

We investigate sectoriality and maximal regularity in L-LSobolev spaces for the structurally damped plate equation with DirichletNeumann (clamped) boundary conditions. We obtain unique solutions with optimal regularity for the inhomogeneous problem in the whole space, in the half-space, and in bounded domains of class C. It turns out that the first-order system related to the scalar equation on...

In this article, the totally geodesic submanifolds in the complex 2Grassmannian G2(C) and in the quaternionic 2-Grassmannian G2(H) are classified. It turns out that for both of these spaces, the earlier classification of maximal totally geodesic submanifolds in Riemannian symmetric spaces of rank 2 published by Chen and Nagano (1978) is incomplete. For example, G2(H) with n ≥ 5 contains totally...

Born’s reciprocal relativity in flat spacetimes is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born’s theory to the case of curved spacetimes and construct a deformed Born reciprocal general relativity t...

We prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov equation ∂tu+∆∂xu+u∂xu = 0 in the Sobolev spaces Hs(R3), s > 1, as well as in the Besov space B 2 (R 3). The proof is based on a sharp maximal function estimate in time-weighted spaces.